BALTICA Volume 24 Number 1 June 2011 : 13-24
The morphology of sand spits and the genesis of longshore sand waves on the coast of the
eastern Gulf of Finland
Daria Ryabchuk, Igor Leont’yev, Alexander Sergeev, Elena Nesterova, Leontina Sukhacheva,
Vladimir Zhamoida
Ryabchuk, D., Leont’yev, I., Sergeev, A., Nesterova, E., Sukhacheva, L., Zhamoida, V. The morphology of sand spits
and the genesis of long–shore sand waves on the coast of the eastern Gulf of Finland. Baltica, 24 (1), 13–24. Vilnius.
ISSN 0067-3064.
Abstract A study of the southern coastal zone of the eastern Gulf of Finland found sand spits up to 1100 m
long and up to 200 m wide, with sand cusps 15 to 100 m wide moving eastward along the shoreline. Similar
morphological forms have been described as long–shore sand waves associated with high energy coasts.
This article presents the results of field geological and geomorphological studies and retrospective analyses
of remote sensing data (air- and satellite photos of on–shore and near–shore parts of the coastal zone). The
development of the long–shore sand waves in the study area is explained by the fact that prevailing waves
induced by the westerly winds propagate almost parallel to the coast. It is shown that under these conditions
the shoreline contours become unstable and any small perturbations to the shoreline extend these contours
with time.
Keywords long-shore sand waves, sand spits, coastal modelling, eastern Gulf of Finland.
Daria Ryabchuk [[email protected]], Alexander Sergeev [[email protected]], Elena Nesterova [[email protected]], Vladimir Zhamoida [[email protected]], A.P.Karpinsky Russian Geological Research
Institute, 74 Sredny pr., Saint Petersburg, 199106; Igor Leont’yev [[email protected]], P.P.Shirshov Institute of Oceanology RAS, 36, Nahimovski prospect, Moscow, 117997, Russia; Leontina Sukhacheva [[email protected]], Institute
of Remote Sensing Methods for Geology, Saint Petersburg, 196140, Pulkovskoye Shosse, 82. Manuscript submitted 10
February 2011; accepted 3 May 2011.
INTRODUCTION
Traditionally the coastal zone of the easternmost
(Russian) part of the Gulf of Finland has not
been considered as an area of active of litho– and
morphodynamics, but recent studies have shown
that locally coastal processes can be quite active due
to the combination of geological and geomorphic
conditions, hydrometeorological and anthropogenic
factors (Ryabchuk et al. 2007, 2009).
One such area with active lithodynamics is located
in the southern coastal zone to the west of the Saint
Petersburg Flood Protection Facility (Fig. 1). Sand
spits of different shapes and size found here are among
the most remarkable morphologic coastal forms of the
eastern Gulf of Finland.
Large accretion forms are common features of the
coast of the Baltic Sea. Many researchers have discussed the processes of formation and development
of huge sand accretion forms in South–Eastern Baltic
such as Curonian Spit, Vistula Spit, Hel Spit (Furmanczyk 1995; Badukova et al. 2006; Povilanskas et
al. 2006; Bitinas et al. 2008; Žaromskis, Gulbinskas
2010). Along the Estonian coast several spits formed
by pebbles and small boulders are described (Suursaar
et al. 2005, 2008; Orviku et al. 2009).
In the easternmost part of the Gulf of Finland active sand accretion areas are the least common type
of coast, and extending spits being even rarer. The
coast of the Vyborg Bay area has many skerries, and
the shoreline configuration is very complicated with
many islands and narrow bays. The northern coast
13
Fig.2. A – giant cusps; B – beach protuberances (Davis
1978); C – cuspate spits; D – long–shore sand waves.
Fig. 1. The study area (red rectangle) in the eastern Gulf of
Finland. 1 – side–scan and echo sounding profiles; 2 – offshore sampling stations; 3 – area of geo–radar study. I – III
– coastal segments with different dynamics.
of the Gulf of Finland to the east of Cape Flotsky is
largely open to the west and is strongly affected by
storms. This, together with a sediment deficit results
in active erosion with annual rates up to 2.5 m year-1.
Stable sand accretion areas are located in the bay heads
of large bays of the southern coast (Luga Bay, Kopora
Bay, Narva Bay) and in the sediment flow discharge
area near Sestroretsk. There are also few small pocket
beaches (Ryabchuk et al. 2011).
The studied coastal zone, in the vicinity of Bolshaya
Izhora village is the only place in the Eastern Gulf
of Finland where active development of sand spits is
found. Very intense dynamics of the area was reported
already by Kaarel Orviku (Orviku, Granö 1992). The
geological description of the coastal zone and the preliminary result of A.P.Karpinsky Russian Geological
Research Institute (VSEGEI) field studies were presented (Suslov et al. 2008). More recent studies using
field observations and the analysis of modern and
archived remotely sensed data (RSD) (aerial and high
resolution satellite images) showed that the processes
of growth and degradation of sand spits are accompanied by the formation of regular sand cusps along
their seaward edges and by their movement eastward
(Ryabchuk et al. 2009).
Different foreshore morphologies were described
in Shepard (1952), Zenkovitch (1959), Dolan (1971),
Davis (1978). Features with regular sinuosity less than
a few hundred meters in wavelength, represented by
alternation of horns and embayed areas are called giant cusps (Shepard 1952) (Fig2A). Having the same
shape as beach cusps, these features are completely
different as beach cusps are much smaller (up to 10 m
and temporal scale of hours to a few days) and they
are characterized by coarse sediment with respect to
the adjacent beach area. Giant cusps do not display
obvious textural patterns across their extent, they have
14
along–shore wavelengths of tens to hundreds meters
and generally exist on a temporal scale of weeks or
months (Davis 1978; Davidson–Arnott, van Heyningen 2003).
The other common type of shoreline rhythmic features are described as beach protuberances (Fig.2B)
after (Goldsmith and Colonell 1970) and have the
same general aerial configuration as giant cusps except
that the shore has a smooth “sine curve” shape (Davis
1978), whereas in giant cusps the apexes are peaked
with the intervening areas smoothly curved. Cuspate
spits (flying spits or “Azov type” spits) (Zenkovitch
1959) (Fig.2C) are elongated with an oblique angle to
the shoreline. Rhythmic coastal features of wave–like
shape––local disturbances to the otherwise mostly
straight beach planforms––characterized by a wide
accretion down–drift end and a narrow, erosion up–
drift end, with the difference in beach width being of
the order of 50–100 m were described by Davidson–
Arnott and Stewart (1987) and are called long–shore
sand waves (Fig.2D). These features have along–shore
scales of the order of tens to thousands meters and a
temporal scale of years to decades (Davidson–Arnott,
van Heyningen 2003).
Long–shore sand waves were observed on sandy
coasts with relatively high energy regimes (California, Long–Island, western coast of Denmark) as well
as on the coasts of some large lakes such as Lake
Erie (Thevenot, Kraus 1995; Davidson–Arnott, van
Heyningen 2003). At the down–drift end of Long
Point (14 km), a 40 km long spit in Lake Erie, seven
to nine sand waves occur. They are 50–100 m wide
at the down–drift end, range in length from 350 m to
>1500 m wide, and migrate along-shore with rates of
100–300 m year-1 (Davidson–Arnott, van Heyningen
2003). Eleven long–shore sand waves with an average
length of 750 m and amplitude (typical width) of 40 m
were identified along Southampton Beach. A 16–month
study calculated yearly average migration speed at 350
m year−1. The migration rate was much higher under
winter wave conditions and reaching an average of
1090 m year−1 (Thevenot, Kraus 1995).
Long–shore sand waves development was explained
in different ways, e.g. by irregularity of the long–shore
drift due to pulsed of river discharge or due to erosion
of sand bars (Thevenot, Kraus 1995), by onshore migration and welding of inner near–shore bars, which is
reinforced by refraction of highly oblique wind waves
(Davidson–Arnott, van Heyningen 2003).
Ashton with co–authors, undertook a numerical
simulation of coastline features, e.g. long–shore sand
waves, and demonstrated that they are forming by
large scale instabilities induced by high–angle waves.
The spatial scales of long–shore sand waves can be
up to hundreds of kilometres and temporal scales
up to millennia (Ashton et al. 2001; Ashton, Murray
2006a, b).
The study area in the Eastern Gulf of Finland has
hydrodynamic conditions essentially different from the
areas discussed above. In contrast to areas where sand
waves have been observed, the Eastern Gulf of Finland
is a region of relatively low–energy. Calculated significant wave heights strongly depend on wind speed
and do not on fetch. Under relatively calm conditions,
the maximum significant wave height does not exceed
0.5 m. The highest (~1.5 m) waves are generally concentrated in the central part during severe storms. For
the strongest westerly storms wave height reaches 2 m
height (Kurennoy, Ryabchuk 2011). The difference in
the magnitude of forcing factors for similar features
is a good reason to study in detail the development of
sand waves in the Eastern Gulf of Finland.
The main objectives of this study are to characterize the litho– and morphodynamics and to provide
an interpretation of the features of the area based on
of field observations and 30 years RSD data analysis using a mathematical modelling approach, with
an aim to explain mechanisms which determine the
long–shore sand wave’s formation and their links to
spit development.
MATERIALS AND METHODS
A geological survey of the Eastern Gulf of Finland
seabed was undertaken by the Department of Marine
and Environmental Geology of VSEGEI from 1980
to 2000. The survey resulted in a set of geological
maps (Amantov et al. 2002; Spiridonov, Pitulko 2002;
Spiridonov et al. 2007; Petrov 2010).
From 2004 to 2010 the VSEGEI undertook research
to understand the geology and morphology of the
coastal zone of the Eastern Gulf of Finland, including near–shore bottom and adjacent on–land areas
(Ryabchuk et al. 2007, 2009; Suslov et al. 2008).
Within the investigated area, annual field observations,
GPS–surveys of the shoreline and systematic sediment sampling of the general appearance of the beach
were undertaken. In 2008, sand spits in the vicinity of
Bolshaya Izhora village were studied using a georadar
SIR System–2000 (GSSI, USA). A 960 m long profile
along the sand spit (20 m landward from the shoreline)
and 5 profiles across the spit were measured (see Fig.1).
To assist the interpretation of radar profiles, seven cores
were drilled using a “Stihl BT 120” earth auger and
sub–sampled at 10 cm intervals. Radiocarbon dating of
sediments (3 samples) using dispersed organic carbon
was performed at the Centre of Isotopic Research of
VSEGEI using an ultra low level scintillation counter,
Quantulus 1220. Radiocarbon data were converted into
calibrated ages using Calib 5.0 (calib.qub.ac.uk/calib)
and the Marine04 curve (Hughen et al. 2004).
Since 2004 annual studies of the bottom relief and
the properties of sediments along four cross–shore
profiles have been undertaken. In 2010 a levelling survey was carried out along the same profiles and along
additional 10 onshore profiles across the easternmost
spit. A PAL Automatic Level (CST/berger, Germany)
was used for levelling surveys. Onshore and bottom
samples were taken. Grain–size analyses of 34 onshore
samples and 26 bottom sediment samples were carried
out in the laboratory of VSEGEI (Department of Marine and Environmental Geology) using an analytical
sieve shaker (AS 200 Retsch, Germany). Sediments
were separated into 21 grain–size classes, and the main
statistical parameters (Md, Ma, So, A) of size classes
were calculated according to suggestions in Folk and
Ward (1957).
In the near–shore zone, over 100 km of side–scan
sonar (CM2, C–MAX Ltd, UK with a working acoustic
frequency of 325 kHz) and echo sounding (GP–7000F,
Furuno, Japan) data were collected enabling 3D plotting of the bottom surface relief in water depths between 1.5 m and 12 m.
The results of field observations were analyzed together with available remotely sensed data (including
aerial photos from 1989 and 1990, with a resolution
of 0.5 m; Quick Bird space pictures from 2004–2007,
with a resolution of 0.64 m) as well as navigation
and topographical charts published in the XIX–XX
centuries.
RESULTS: LITHO– AND MORPHO­
DYNAMICS
The upper 50 m of geological sequence within the study
area is comprised of Late Pleistocene and Holocene
clays and sands. In the near–shore the thickness of
Quaternary deposits increases as a paleo–valley 80 m
deep is located along the shoreline (Spiridonov et al.
2007). The modern tectonic regime is characterized
by low amplitude tectonic sinking with rates varying
from 0 to 2 mm year-1) (Yaduta et al. 2009).
Long–shore sand drift in an eastern direction at a
99% level of significance was established (Suslov et
15
Fig. 3. The underwater topography of the nearshore terrace.
I – III – coastal segments indicative of different dynamics.
al. 2008) using the MacLaren method (Mac Laren,
Bowles 1985) and this accounts for the spatial changes
in the grain–size. Also, in the area of sand spit growth
the direction of the long–shore sediment flow is clearly
morphologically determined by the shape of sand accretion forms and the eastward orientation of small
rivers and rivulet mouths.
The surface of the near–shore bottom is covered by
fine to medium grain–size sand. This material forms
an along–shore sand terrace up to 2 km wide and up
to 3-4 m thick. Seawards, the slope is relatively high
(Fig. 3). The terrace is located in front of the sand spit
area and is elongated 8 km to the west. The long–shore
submarine terrace plays an important role in coastal
development of the area. Firstly, submarine terraces
recognized along the northern coast of the Eastern Gulf
of Finland at the same water depth (4-5 m) (Ryabchuk
et al. 2007) and most probably formed during the Late
Holocene as a result of both coastal recession and sediment accumulation (Leontyev et al. 2010) may protect
the shores from the most intense erosion events. Secondly, unlike the terraces of the northern coastal zone,
the sand accretion terrace in front of Bolshaya Izhora
village gradually transforms into a sandy near–shore
coastal slope. Therefore, the terrace may be one of the
sources of material for the sand spit formation.
According to dominating lithodynamic processes,
the study area can be divided into three segments according to dominant lithodynamic processes: a straight
coastal section elongated from east to west where intense erosion prevails (I in Fig. 1); the central part of
study coastal zone between the shoreline orientation
change and the River Tchernaya mouth where wide
sand spits and long–shore sand waves are observed
(II in Fig. 1); the sand spit to the east of the River
Tchernaya, which is rapidly growing at its distal edge
(III in Fig. 1).
To the west (I in Fig.1), along the straight coastal
segment, sandy beaches are not wider than 10–12 m.
Beaches comprise medium to poorly sorted (sorting
value – the standard deviation of the relevant grain–size
distribution (So) is about 1.5–2.6) medium–grained
sands (mean grain–size ~ 0.47 mm), sometimes with
a high gravel content (up to 25%). On the backshore,
low cliffs (up to 5–7 m) were formed by the early 1980s
Fig. 4. Erosion of the coastal cliff to the west of Bolshaya Izhora village. A – rate of shore cliff erosion in 1990–2006;
B – the coastal cliff (I at Fig. 1).
16
gradually becoming shallower and overgrowing with
water plants. The coastal
landscapes indicate that
the coastal dynamics have
been relatively unchanged
for hundreds of years as
demonstrated by the shape
and size of relict spit (I in
Fig. 5A). It is up to 10 m
maximal height, 920 m long
and up to 112 m wide. This
relict spit is sub parallel to a
recent sand body of the similar shape, located eastward
(II in Fig.5A).
Along the seaward edge
of the contemporary marine
sand spit long–shore sand
waves occur. An important
feature of the sand cusps
is an increase in the size
(length and width at the
down–drift end) in the eastern direction. The width of
the down–drift end of the first
(western) cusp is 15 m, with
an adjacent strait shoreline
segment 100 m long. The
second cusp has an amplitude
30 m and length 250 m; for
the third and forth (eastern)
cusps these parameters are
70 m and 400 m and 100
m and 900 m, respectively
Fig. 5. Alternation of erosion, transit and accretion areas in the vicinity of Bolshaya Izhora (Fig. 6).
The described morphovillage (A) and coastal profiles of accretion (B) and erosion (C) zones (II in Fig. 1).
logical features reflect differ(Orviku, Grano 1992) as a result of intense erosion. ent lithodynamic zones: transitional (straight coastal
RSD analysis shows that the rate of shoreline retreat is segments), accumulative (seaward protrusion at the
distal parts of cusps), and erosional (concave sections
up to 0.6 m year-1 between 1989 and 2007 (Fig. 4), and of the shoreline, adjacent to the accretion areas to the
the erosion of sandy cliffs may be the second source of east). Annual shoreline GPS–surveys have shown that
sediments for down–drift sand spit accretion area. The the western cusp (Fig. 6) moved eastward 33 m since
submarine coastal profile is steep near the shoreline (a 2007 to 2009, and the adjacent cusp migrated by 26 m
depth of 1.5–1.8 m is reached at the distance of 7–10 during the same time. Retrospective analysis 15 years
m from the shoreline), but further offshore slope is of remote sensing data (1989 to 2004) shows shifts of
more gentle and gradually transforms into surface of 315 m and 200 m. The average annual shifts of cusps
-1
-1
a submarine terrace. The smooth bottom surface com- were 20 m year and 13 m year correspondingly. Such
prises well–sorted fine–grained sands (mean grain–size sand cusp movement causes the alternation of erosion
and accretion along the coast (Fig. 5A). For example,
~ 0.14 mm, So ~ 1.5).
The coastal segment to the east (II in Fig. 1; in on cross shore profiles located within down–drift parts
of sand cusps, between 1990 and 2007 shorelines
front of Bolshaya Izhora village) has much more moved 80-110 m seaward, while in the erosion zone
complicated dynamics with long–term development the shoreline moved 70 m landward (Fig. 6). It is
of sand spits some hundreds meters long and some important to keep in mind, as in such a case observatens of meters wide. In the vicinity of Bolshaya Izhora tions at a single point may give misleading results and
village the maximal width of the area of relict sand for the proper understanding of coastal processes the
spits and lagoons reaches about 500 m. The spits have entire system of cusps should be analysed in terms of
separated from the open sea; small narrow lagoons are planforms.
17
the shoreline. On the eroding parts of the sand waves,
low escarpments in the relict sand spits are located
at a distance of 6–10 m from the shoreline (Fig. 5C).
The grain–size of the eroding beach sands is similar
to that of the distal part of sand waves (medium–
grained sands, average diameter of 0.4–0.5 mm, So
1.59–2.83).
Submarine coastal profiles are very flat along the
length of the spits (Fig. 5B, C), however, the shoreward
100 m of the eroding profiles is shallower than on accreting profiles. This can be explained by very high
shoreline shift rate, due to which the coastal profile
have not reached an equilibrium state. The near–shore
bottom is covered by well–sorted (So 1.0–1.5) fine–
grained (average grain–size 0.2 mm) sands; but along
the shoreline outcrops of clay sediments are observed
on the sea bottom surface.
Another set of coastal features n study area are sand
spits that grow from initial shoreline disturbance, with
the formation of elongated lagoon (so called connected
spits). An example of these features are large (500 m
long) accretion sediment deposits which formed as a
result of sediment discharge in the eastern part of the
study area, to the west of the Tchernaya River mouth,
over the last 30 years (Fig. 7A). The topographic chart
Fig. 6. Long–shore sand waves development based on remote sensing data analysis (II in Fig. 1). A – development
of 500 m long sand accretion body from 1982 to 2007; B
– forming of 50 m connected spit in 2009–2010 (red rectangle, Fig. 6A); C – area of active erosion after 2006–2007
winter storms.
Fig. 7. Formation of connected spits: A – 500 m long sand
body to the west of the Tchernaya River mouth; B – transformation of long–shore sand waves into connected spits
(2007–2010).
Morphology and sediment data for the coastal profile, obtained annually for five years has shown that
areas of sediment accretion, transit and erosion have
some special features of note. At the “distal” ends of
sand waves the width of the spits reach 70–80 m, with
a height of 2 m (Fig. 5B). The sediments of the beach
face have average 40–60% sand in the dominant class
of 0.25–0.5 mm. The average grain diameter is 0.55
mm. The majority of the samples are represented by
medium to poorly sorted sand (So 1.5–2.3). After storm
events 0.5–1.0 m beach cusps of coarse–grained sand
and gravel (up to 60% particles > 2.0 mm) form along
from 1982 showed a smooth curve of the coastal line.
The topographic chart from 1986 fixed the beginning
of sand spit growth and lagoon formation. Aerial photography from 1989 showed the formation of a narrow
sand bridge between the spit ridge and the river delta,
and the lagoon being closed. The satellite photo and
field GPS–study from 2005 showed that the sand spit
was quite wide and a dry lagoon. By 2005 the sand
body was entirely formed with the former lagoon being
since 2009 a dry low space overgrown with grass and
shrubs. It is interesting to notice that but the same process at a smaller scale was observed during 2008–2010
18
(Fig. 6B). Long-shore sand waves started to transform
into connected spits (Fig. 7B).
To the east of the river mouth is located a spit with
quite a complicated shape. The width of the spit varies from 30 to 90 m; its maximal height is 2.5 m. The
length of the spit (in 2010) was 1100 m (Fig. 8, 9).
Georadar profiling data confirmed by drilling showed
sediments are observed along the shoreline. They have
outcropped here as a result of intense erosion. In front
of the central part of the spit relict lagoon marl is outcropping on the sea bed about 100 m from the present
shoreline, at the depth of 0.5–0.8 m (Fig. 10).
The distal end of the spit is still growing, while the
western (attached) part of the spit is intensely eroded.
Retrospective analysis of remote sensing data (Fig. 9)
has shown that since 1990 the attached part of the sand
spit shifted more than 100 m landwards. Erosion of
the attached parts of spits accompanied by the growth
Fig. 8. Geo–radar profiles of the distal part of the spit.
1 – coarse–grained poorly sorted sands; 2 – fine–grained
medium sorted sands; 3 – coarse–grained sands with pebbles
and gravel; 4 – clayey black mud with remains of plants;
5 – 7 – geophysical boundaries confirmed by drilling; 8 – 9
– geophysical boundaries.
Fig. 9. Development of a hooked sand spit to the east of the
Tchernaya River mouth.
the upper sediment layer of the spit comprising coarse–
grained (average grain–size 0.7–0.9 mm), poorly sorted
(So 2.7–3.46) sands.
The thickness of this sand layer varies from 150 cm
at a distance of 10–12 m from the shoreline to 205–245
cm along the spit crest. The fine fraction component
(<0.01 mm) is less than 0.2% and in some horizons
the content of gravel is relatively high (8–26%). Some
cores had layers of fine–grained (average grain–size
0.2 mm), better sorted (So 1.5–2.0) sand up to 0.5 m
thick (Fig.8).
At the core interval 180–245 cm (depending of the
core location) sands overlap black dense silty clays
with a high content of organic matter and the remains
of plants which are interpreted as relict lagoon marl.
Along the western part of the sand spit, the same
Fig. 10. Sand spits of different generation in the vicinity of
Bolshaya Izhora village. 1 – modern sand spits; 2 – ancient
sand spits; 3 – relict sand spits; 4 – relict lagoons; 5 – sites
of sampling for 14C dating. Pictures of relict lagoon marl.
19
formed in the Post–Litorina time. It is improbable that these s
that time in shallow water conditions near the coast of the ope
deposits are likely to be marl formed within small ancient lag
thespits
waves
propagate
perpendicularly to the
of the distal parts is typical for many spits worldwide by
lately
eroded almost
and disappeared.
(Dolotov et al. 1964; Zhindarev, Khabidov 1998; Chen coast, while in the second case they run almost along
Modelling
studies
by Ashtonfunction
et al. (2001);
Ashton
the shore. The
trigonometric
on the right
in and Murray
et al. 2002).
DISCUSSION – THE
DISCUSSION
GENESIS OF
– THE
THEGENESIS
LONG–SHORE
LONG–SHORE
WAVES
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Eq. (2) OF
canTHE
beSAND
expressed
in the SAND
first case
as
(2006) (lead
to 2conclusion
that
possible
mechanism
the
N – THE GENESIS
OF THE
LONG–SHORE
SAND
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and
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and
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DISCUSSION
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It is GENESIS
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SCUSSION DISCUSSION
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OF
THE
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.
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with
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LONG–SHORE
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o determine It
sand
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and
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DISCUSSION
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THE
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the
equation,
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/ in
∂the
y(3)
(Θ
/the
sin
, and
inbodies.
second
as
relict
lagoons
relict
(Fig.
spitscase
10).
relict
lagoons
(Fig.
10).
Radiocarbon
of
four
samples
dating
of
relict
of
samples
(SAND
1 / 2) sin 2WAVES
Θ
+ ∂χspits
/ ∂y , of
2))sin
sin 22represented
Θ +−represented
possible to determine
sand
different
generations
recent
and
sand
bodies.
The
represented
in
the
of the
diffusion
ONG–SHORE
and
inform
the second
case as ((11equation,
Then
Eq.
(3)
be
the
of can
the diffusion
// 2–
Θ
∂∂χχ // ∂∂relict
yy .inand
/ 2)equation,
sin 2Θ − ∂χ / ∂y . Then Eq. (3) c
theform
second
case
asKF(1equation,
2form
in
the
the
diffusion
χof ,Eq.
χcan
∂perturbations
∂in
ofofof
shoreline
contour
tend to
grow∂over
tim
1 / 2It) sin
2possible
Θ + ∂χ (Fig.
/ ∂yto, and
(1of/ 2different
) sin
2small
Θ − ∂samples
χinitial
/ ∂y .represented
2
inthe
the
second
case
as
Then
(3)
be
lict spits (relict
10).
Radiocarbon
dating
of10).
four
islagoons
determine
spits
inthe
the
form
of
the
diffusion
equation,
ν
=
ν
=relict
±represented
χ
∂χ
represented
in
form
the
diffusion
equation,
represented
in
form
oflagoons
the
diffusion
equation,
oldest
relict
spits
relict
(Fig.
Radiocarbon
dating
of
four
samples
of
relict
represented
in
the
form
of
the
diffusion
equation,
,
,
2 sand
It
is
possible
to
determine
sand
spits
of
different
generations
–
recent
and
relict
sand
bodies.
The
in
the
form
of
the
diffusion
equation,
2
2and
2
KF
DISCUSSION
–
THE
GENESIS
OF
THE
LONG–SHORE
SAND
WAVES
lagoon
mud
(time
interval
lagoon
are
mud
overgrown
(time
interval
by
pine
are
forest,
overgrown
separated
by
pine
forest,
by
low
and
elongated
separated
by
low
elon
DISCUSSION
–
THE
GENESIS
OF
THE
LONG–SHORE
SAND
WAVES
represented
in
the
form
of
the
diffusion
equation,
χ
χ
∂
∂
KF
ν
=
±
χy ∂diffusion
∂. χ∂Then
h + KF
zc
form
of∂ the
,
oldest
relict
(Fig.
10). case
Radiocarbon
dating
of
t ∂samples
tOF
generations
recent
Theνas=(1the
∂(3)
(1 generations
/ 2–)spits
sin 2Θrelict
+and
∂–χ recent
/ lagoons
∂relict
y , and
/ 2)represented
sin
2Θ − ∂χin
/ ∂the
yfour
χof relict
in
thebodies.
second
can
be νequation,
and
relict
sand
bodies.
oldest
=sand
±WAVES
= (3),
THE
LONG–SHORE
SAND
νEq.
=∂χ±χbe
,
in the
form
the
diffusion
equation,
(3),∂tevolution
, of, coastline
ν =∗ KF
∂y 2 prop
2ν
ν2∂ ,∂2 22χon
= ±based
this
feature
can
22 , forest,
, the
2 equation
KF
mud
(timerepresented
interval
are
overgrown
pine
and
separated
by
low
elongated
KF
h
+
z
KF
χ
∂
χ 2of
χby
∂mud
∂by
∂
t
χ
χ
∂
∂
∂
y
h
+
z
KF
∂
t
∂
y
χ
χ
∂
∂
∗
c
2
lagoon
(time
interval
are
overgrown
by
pine
forest,
and
separated
by
low
elongated
h
+
z
relict
spits
are
overgrown
pine
forest,
and
separated
oldest
relict
spits
relict
lagoons
(Fig.
10).
Radiocarbon
dating
of
four
samples
of
relict
∗
c
∂14t C
νbodies.
=C
KF
ν y2and
∗
cbodies.
ν÷(3),
=14
ν spits
=
χinterval
χof
∂of
∂to
Itdating
is
possible
toform
determine
spits
ofpine
generations
recent
and
relict
sand
,BPand
νdifferent
=that
ν±low
= =±
νthe
=are
±
=overgrown
±νprobably
χthe
∂χ1800±170
∂ –
It(time
is possible
determine
of different
generations
–from
recent
and
relict
sand
The
, ,±KF
,=years
,sand
, probably
(3),
represented
in
the±
diffusion
equation,
,sand
, and
ν(414
Θ , year
2=
swamps
that
swamps
are
former
from
1800±170
BP
776
years
cal.
(414
AD)
776 cal.
resp
where
“+”
“−“
correspond
toνThe
small
large
, ÷ angles
mud
by
Radiocarbon
samples
2 of
ν2relict
=sand
∂signs
tbyyears
(3),
KF
s oflagoon
different
generations
relict
ν former
=separated
±are
h,∗ former
+ hzforest,
χ elongated
χ–ν∂recent
∂low
∂ 2=four
+ zrelict
t swamps
∂ν∂y∂ty=elongated
∂y that
,2 , h∗hν∗+ +z cz c h∗ +
(3), “
by
probably
are
∂
y
z
where
the signs “+” and
2∂t, and
c∗ The
∂
y
14h + zbodies.
c1956)
2 ,∂t
c
ν
=
∂
t
∂
y
14
ν
=oldest
±
h
+
z
Θ
,
respectively,
and
is
the
where
the
signs
“+”
and
“−“
correspond
to
small
and
large
angles
∂
t
that probably
are
former
from
1800±170
C
years
BP
(414
÷
776
cal.
years
AD)
∂
y
,
,
(3),
∗
c
Θ
,
respe
where
the
signs
“+”
and
“−“
correspond
to
small
and
large
angles
where
the
signs
“+”
and
“−“
correspond
to
small
and
2
SION
– THElagoons
GENESIS
OF
THE
LONG–SHORE
SAND
WAVES
∗
c
Θ
2
where
the
signs
“+”
andfour
“−“776
correspond
small
and large angles , re
lagoon
mud
(time
are
overgrown
by
pine
forest,
and
separated
by
low
elongated
14 hinterval
14Radiocarbon
that
probably
are
former
from
1800±170
C
years
BP
(414
÷
years
AD)
spits
relict
(Fig.
10).
dating
of
four
samples
of cal.
relict
diffusion
coefficient.
KF
(Fig.
10).
Radiocarbon
of
four
14samples
χare
+lagoons
zdating
∂and
t∂χ swamps
y∂ relict
oldest
relict
spits
(Fig.
10).
Radiocarbon
dating
of
samples
oftotorelict
2500±150
tolagoons
2500±150
years
BP
cal.
C
years
years
BP
–large
(632
151
cal.
years
BC
AD))
–and
151
showed
cal.
that
years
itdiffusion
AD))
was
showed
that
itre
∗relict
c1800±170
byswamps
pine(110).
forest,
by
low
elongated
that
former
C
years
(414
÷the
776
cal.
years
AD)
ν from
=C
coefficient.
νand
ns
(Fig.
Radiocarbon
dating
of
four
samples
of
relict
,r
where
the
signs
“+”
and
“−“
correspond
small
andsmall
large
angles
ν/∂to
±where
ΘΘ,ang
Θ
,Θ
respectively,
and
is
the
diffusion
large
angles
Θ
2relict
Θprobably
+=
∂separated
χlagoon
∂ydiffusion
(1correspond
/(632
2) sin to
2Θsmall
−to
∂by
χsmall
/ BP
∂diffusion
y∂BC
,mud
,“−“
where
signs
“+”
and
“−“
correspond
tothe
small
and
large
angles
,(3),
respectively,
is νthe
the
signs
“+”
and
“−“
correspond
and
large
angles
,
respectively,
is
where
the
signs
“+”
and
and
angles
,
in
the
second
case
as
.
Then
Eq.
(3)
can
be
where
the
signs
“+”
and
“−“
correspond
to
and
large
2and
14 / 2) sin
χ
1
∂
Q
ν
coefficient.
of
(time
interval
are
overgrown
coefficient.
Θ
,
respectively,
and
is
the
where
the
signs
“+”
and
“−“
correspond
to
small
and
large
angles
h
+
z
Θ
14
∂
t
diffusion
coefficient.
∂
y
,
respectively,
an
where
the
signs
“+”
and
“−“
correspond
to
small
and
large
angles
14
±150
C14years
BP
(632
cal.
years
BC
–
151
cal.
years
AD))
showed
that
it
was
∗
c
χ
=
a
sin
ky
ble to determine
sand
spits
of
different
generations
–
recent
and
relict
sand
bodies.
The
Let
a
small
wave–like
perturbation
of
amplitude
a,
leng
lagoon
mud
(time
interval
are
overgrown
by
pine
forest,
and
separated
by
low
elongated
=
to
2500±150
C
years
BP
(632
cal.
years
BC
–
151
cal.
years
AD))
showed
that
it
was
(
1
/
2
)
sin
2
Θ
+
∂
χ
/
∂
y
(
1
/
2
)
sin
2
Θ
−
∂
χ
/
∂
y
swamps
that
probably
are
former
from
1800±170
C
years
BP
(414
÷
776
cal.
years
AD)
coefficient.
ν
,
and
in
the
second
case
as
.
Then
Eq.
(3)
can
be
14
Θ
,improbable
,diffusion
respectively,
and
is
where
the
signs
“+”
and
“−“
correspond
to
small
large
angles
lagoon
mud
(time
interval
are
overgrown
byAD))
pine
forest,
and
separated
by
low
elongated
diffusion
formed
in
the
Post–Litorina
in
time.
the
ItPost–Litorina
time.
that
Itthese
sediments
that
could
these
accumulate
sediments
couldwave–li
accum
pine
forest,
and
by
lowformed
elongated
swamps
Letin
a small
coefficient.
diffusion
coefficient.
diffusion
e00±170
overgrown
by
pine
forest,
and
separated
by
low
elongated
C years
BP
(414
÷separated
776
cal.
years
AD)
to 2500±150
C
years
BP
(632
cal.
years
BC
–and
151
cal.
showed
that
it the
was
represented
in
the
form
of
the
diffusion
equation,
diffusion
coefficient.
∂14tΘky
+small
zacoefficient.
∂wave–like
yisa,
χisyears
=improbable
a sin
λperturbation
= χa sin
Let
acoefficient.
small
wave–like
perturbation
ofhamplitude
length
and
wave χnumber
diffusion
coefficient.
Let
small
perturbation
a, length
= aky
sinof
kyamplitude
∗a
csmall
14and large
ofamplitude
Let
wave–like
diffusion
coefficient.
Let
wave–like
perturbation
of
le
ν
,
respectively,
and
is
the
where
the
signs
“+”
and
“−“
correspond
to
small
angles
C
years
BP
that
probably
are
former
from
1800±170
14
n
the
Post–Litorina
time.
It
is
improbable
that
these
sediments
could
accumulate
in
χ
=
a
sin
kya, in
k
=
2
π
/
λ
appear
on
the
shoreline
contour.
Substitution
of
st relict spits
relict
lagoons
(Fig.
10).
Radiocarbon
dating
of
four
samples
of
relict
represented
in the Let
form
of
the
diffusion
equation,
swamps
that
probably
are BP
former
from
1800±170
C
years
BP
(414
÷
776
cal.
years
AD)
diffusion
coefficient.
14cal.
formed
in
the
Post–Litorina
time.
It
is
improbable
that
these
sediments
could
accumulate
in
to
C
years
(632
cal.
years
BC
–
151
years
AD))
showed
that
it
was
χ
=a kasin
sin
ky
2 2500±150
Let
a
small
wave–like
perturbation
of
amplitude
a,
l
χ
=
ky
χ
=
a
sin
ky
14
χ
=
a
sin
ky
λ
Let
a
small
wave–like
perturbation
a
small
wave–like
perturbation
of
amplitude
a,
len
of
amplitude
a,
length
and
wave
number
λ
=
2
π
/
λ
14
Let
a
small
wave–like
perturbation
of
amplitude
a,
length
and
wave
number
appear
on
the
and
wave
number
amplitude
a,
length
χ
=
a
sin
ky
swamps
that
probably
are
former
from
1800±170
C
years
BP
(414
÷
776
cal.
years
AD)
that
time
in
shallow
that
water
time
conditions
in
shallow
near
water
the
coast
conditions
of
the
near
open
the
sea.
coast
Therefore
of
the
open
these
sea.
Therefore
thes
KF
Let
a
small
wave–like
perturbation
of
ampl
χthe
χ
∂776
Cayears
(414
÷toperturbation
776
years
mer
formed
in∂(414
Post–Litorina
It
is
improbable
that
could
accumulate
in
BC
–from
1511800±170
cal.
years
AD))
that
it2500±150
was
BP
cal.
years
AD)
χC
= AD)
ayears
sin kythese
λ
=appear
a sin
ky
Let
wave–like
of
amplitude
a,
length
and
wave
number
χ (3)
=contour.
aleads
sincontour.
kytoof
ksmall
=showed
2πBP
/14ν
λtime.
χofto
= χagradient
sin
on
thecal.
shoreline
contour.
Substitution
of
into
the
Let
aksediments
small
perturbation
amplitude
a,
length
and
w
= k2π=wave–like
/the
appear
onof
the
shoreline
Substitution
of
=appear
=λaky
sininto
ky
diffusion
coefficient.
ν small
= ±a÷
2λ
π
/χspeed
λand
∂
χ
/
∂
t
on
the Eq.
shoreline
Substitution
2
,
,
(3),
which
links
shoreline
displacement
equation
for
the
perturbation
amplitude
a,
2
χ
=
a
sin
ky
appear
on
the
shoreline
contour.
Substitution
of
KF
λ
Let
wave–like
perturbation
of
amplitude
a,
length
wave
number
eon
in mud
shallow
water
conditions
near
the
coast
of
the
open
sea.
Therefore
these
χ
χ
∂
∂
to
C Post–Litorina
years
BP
(632
cal.
years
BC
–the
151
cal.
years
showed
that
it contour.
was
(time
are
overgrown
by
pine
forest,
and
separated
by
low
elongated
hνcal.
zwater
cal.
years
BC
–the
151
years
AD)
showed
that
itSubstitution
∂(632
t interval
y±2500±150
=a asin
sinky
14
that
in
shallow
coast
of
the
open
sea.
these
k=151
=2χ
2of
π=formed
/aχλ
∗on
con
time.
Itlikely
isnear
improbable
that
these
sediments
could
accumulate
in
on
theTherefore
shoreline
contour.
Substitution
equation
for
χ χ=perturbat
sin
=AD))
aky
sin
ky
π
/ancient
λ
kνcal.
=time
2kπ2years
/,in
λ2πconditions
=+
appear
on
the
shoreline
ofofthe
appear
the
shoreline
contour.
Substitution
of
into
Eq.
(3)
leads
to
the
=
/are
λthe
appear
the
shoreline
contour.
into
Eq.
(3)
leads
to
the
=∂formed
χky
kinto
=appear
2Eq.
πEq.
/lagoons
λ
,conditions
(3),
appear
on
the
shoreline
contour.
Substitution
of
deposits
likely
to
deposits
be
marl
are
formed
to
be
small
marl
within
small
separated
ancient
from
lagoons
separated
from
to
2500±150
C
years
BP
(632
cal.
years
–sea.
cal.
years
AD))
showed
itSubstitution
was
32 that
cal. years
BC
AD))
showed
that
itcoast
was
χ a,
=kequation
alength
sin
ky
equation
for
the
perturbation
amplitude
time
shallow
water
the
of
the
Therefore
these
probable
thatin
these
could
accumulate
in
(3)
leads
to
the
equation
the
k∂–formed
=
πsmall
/λ
appear
on
shoreline
Substitution
of
into
(3)
leads
to
the
equation
for
the
perturbation
amplitude
a,that
χthe
=for
asea
sin
ky into Eq.
χ
=
ais
sin
ky
k a,
=amplitude
2πwithin
/open
λBC
λfor
appear
on
the
shoreline
contour.
Substitution
of
(3)
le
Let
a2sediments
wave–like
perturbation
of
and
wave
number
the
perturbation
amplitude
a,
h∗ near
+time.
z ccontour.
was
in
the Post–Litorina
It
improbable
t 151
∂
y
∂
a
2 leads tocould
=/Θa∂sin
kyequation
14 Itlagoons
k to
=the
2be
π signs
/λ
appear
on
the
shoreline
contour.
Substitution
ofa,
the
formed
in“−“
the
Post–Litorina
time.
is a,improbable
that
these
sediments
accumulate
in sea
∂χseparated
Q
h∗ i
are likely
marl
formed
within
small
ancient
from
the
sea
νand
(t
isinto
the
the
isfrom
directed
along
=Eq.
mtime
νfor
k(3)
aopen
∂athe coast,
the
perturbation
amplitude
a,the
.perturbation
,yperturbation
respectively,
and
isfor
the
where
“+”
and
correspond
to small
and
large
angles
amplitude
a,y–axis
mps
that
probably
are
former
from
1800±170
C
years
BP
(414
÷
776
cal.
years
AD)
2
equation
for
the
amplitude
a,
equation
for
the
perturbation
amplitude
equation
for
the
perturbation
amplitude
deposits
are
likely
to
be
marl
formed
within
small
ancient
lagoons
separated
that
time
in
shallow
water
conditions
near
the
coast
of
the
sea.
Therefore
these
that
these
sediments
could
accumulate
in
that
time
in
equation
the
perturbation
amplitude
a,
∂
a
=
m
ν
k
a
∂perturbation
a∂separated
ime.
It is improbable
that
these
sediments
could
accumulate
in
.
by
spits
lately
byto
and
spits
lately
eroded
disappeared.
formed
in
the
Post–Litorina
time.
It
is
improbable
these
sediments
could accumulate in
forbe
the
perturbation
a,disappeared.
t that
2
equation
the,ky
amplitude
a,sea
deposits
to
marl
within
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aves
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end
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angle
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11b
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11c
show
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sediment
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along
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Figs.
11b
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1956)
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based
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of
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angle
large.
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11b
11c
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schematically
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aproposed
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this
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will
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the
6) evolution
stline
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general
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of
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evolution
proposed
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1956)
angle
is
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11b
and
11c
show
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Figs.
11b
and
11c
show
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Figs.
11b
and
show
schematically
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variations
in
sediment
fls
Figs.
11b
and
11c
show
schematically
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sediment
flux
Q
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=
=
Figs.
11b
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11c
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schematically
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sediment
flux
Q
along
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a
is
the
initial
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at
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and
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Figs.
11b
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11c
show
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,
,
(1),
(1),
uation
of
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evolution
proposed
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(Pelnard–Considere
0
Θ + δ for
for
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approach
angles.
According
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Eq.
(2),
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Q reaches
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оand
1 ∂of
Q surface–water
Figs.
11bdifferent
11c
show
schematically
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variations
in
sediment
flux
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along
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shoreline
for
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to Θ
Eq.
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Q reaches
itsth
Figs.
11b
11c
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schematically
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variations
sediment
flux
Q along
mpact
waves
approaching
the
coast
aof
high
angle
.Hence,
In“+
cases
in
sediment
Qshoreline
along
the
shoreline
different
χtheand
1and
∂zQ
∂feature
=45
.evolution
ifflux
the
angles
small,
theAccording
increase
in
1956)
∂
t
h
+
∂
y
∂
t
h
+
z
∂
y
angle
is large.
о + δ along the conto
1956)
a
∗
c
∗
c
this
can
be
based
on
the
equation
coastline
proposed
by
(Pelnard–Considere
is
initial
value
of
a
at
the
moment
t=0
and
the
signs
“−”
and
“
correspond
to
Here
Figs.
11b
11c
show
schematically
the
variations
in
sediment
flux
Q
along
the
0
,
(1),
=45
. Hence,
if
the
angles
∂Q angles
∂χ small 1and large
for
different
wave
approach
angles.
According
to
Eq.
Q
reaches
δ(2),
direction
(Fig.
11a).
The
contour
curvature
angle
suppose
Θto
+
δEq.
for
different
wave
approach
angles.
According
to
Eq.
Qare
reaches
itsits
for= different
waveif
angles.
According
to that
Eq.
(2),
Q
reaches
its
maximum
when
Θ
+(2),
δand
for
wave
approach
According
towave
Eq.
Q
reaches
its
maximum
оΘ
,approach
(1),
for
different
wave
angles.
According
Eq.
rem
approach
angles.
According
Q
reaches
оδ
Θоdifferent
respectively.
The
result
(Eq.(5))
means
the
shoreline
perturbation
+(2),
=45
., Hence,
theangles.
angles
areangles.
small,
the
increase
in
along
the
contour
results
in
ofQin
Θ
δ(2),
=45
. Hence,
if
the
angles
are
small,
the
increase
along
the(2),
contou
+ z c ∂=
y
Θ
+ small,
δwhen
for
different
wave
approach
According
to
Eq.
(2),
Q
reaches
its
maximum
when
Θ
+
δtomaximum
=45
. explanation
Hence,
if(1),
the
angles
areapproach
the
increase
in+shoreline
along
theQwh
con
for
different
wave
approach
angles.
According
togrowth
Eq.
(2),
reaches
its
,χ and
∂
t
h
+
z
∂
y
Figs.
11b
11c
show
schematically
the
variations
in
sediment
flux
Q
along
the
shoreline
dQ
/
dy
>
0
о
sediment
flux,
(Fig.11b).
Accordingly
the
disturbanc
al perturbations
of
shoreline
contour
tend
to
grow
over
time.
A
simple
of
∗
c
о
1
∂
∂
Q
о
о
Θ
+
δ
for
different
wave
approach
angles.
According
to
Eq.
(2),
Q
reaches
its
maximum
when
χ=45links
1 о.the
Q
maximum
when
=45
Hence,
if
the
are
Θ∂,if
small
angles
respectively.
The
result
(Eq.(5))
means
shoreline
perturbation
оthe
∂t willh∗decay
+ z1956)
∂the
yо∂large
Θ
δ∂along
.with
Hence,
the
angles
increase
in
along
∂that
χgrow
∂. tδHence,
χ
/are
∂in
t. small,
dQ
dycon
>co
Θδ
+ +=
δflux,
Θits
+=45
δ=45
sediment
if
the
angles
are
small,
the
increase
.=45
Hence,
theifdQ
angles
are
small,
the
increase
in
along
the
contour
results
growth
of
to
gradient
ofif∂growth
long–shore
to(1),
gradient
sediment
of
flux
speed
which
of
shoreline
links
the
displacement
speed
of
displacement
Θ/the
+
angles
are
small,
the
increase
in
along
contour
results
growth
ofδangles
c and
Θ
+the
=45
.if
Hence,
the
angles
small,
the
increase
inχ
о + it
ifwhich
angle
of
incidence
is
small,
and
vice
versa,
will
time
if
the
δthe
≈
≈inlong–shore
tg
/ results
∂sedime
y/δthe
= =sediment
/small,
dy
>
0the
allowing
to
the
use
of
approximations
. alo
Θ
δshoreline
=45
. Hence,
if wave
theHence,
angles
increase
in
along
the
contour
results
ofin
dQ
/dQ
dy
0inthe
flux,
(Fig.11b).
Accordingly
the
shoreline
disturbance
is
suppressed
the
,the
, ∂χare
(1),
sediment
flux,
(Fig.11b).
Accordingly
the
shoreline
disturbance
Θby
+sin
δ along
=45
. Hence,
ifsediment
the
angles
are
small,
inare
the
contour
in
/>coastline
dy
>+
0 increase
flux,
(Fig.11b).
Accordingly
shoreline
disturb
small,
the
increase
in
along
the
contour
results
in
Θ
δ
for
wave
approach
angles.
According
to
Eq.
(2),
Q
reaches
its
maximum
when
о different displacement
/
∂
t
sediment
flux
and
the
tends
to
straighten.
(1),
(1),
to
gradient
of
long–shore
sediment
flux
e speed
of
shoreline
h+∗ z+
zare
∂small,
y /incidence
∂links
t∂iftthe
hangle
∂cof
ydQ
+ δvice
=45
. Hence,
the
the
increase
in Θ
along
the
contour
results
in
growth
of0 (Fig.11b).
can be
based
on the
equation
coastline
evolution
proposed
by
(Pelnard–Considere
will
decay
if
wave
is
small,
and
versa,
will
grow
with
time
if
the
∂χthe
/it∂shoreline
tsediment
∗angles
cof
to
gradient
of
long–shore
sediment
flux
which
the
speed
of
shoreline
displacement
dQ
/
dy
>
(1),
flux,
Accordingly
the
shoreline
disturb
sediment
flux
and
the
coa
dQ
/
dy
>
0
dy
>
0
dQ
/
dy
>
0
sediment
flux,
(Fig.11b).
Accordingly
the
shoreline
disturba
sediment
flux,
(Fig.11b).
Accordingly
disturbance
is
suppressed
by
the
sediment
flux,
(Fig.11b).
Accordingly
the
shoreline
disturbance
is
suppressed
by
the
dQ
/
dy
>
0
growth
of
sediment
flux,
(Fig.11b).
Accordangle
is
large.
χ
1
∂
∂
Q
sediment
(Fig.11b).
Accordingly
theisshorelin
χis /the
∂in
t is
о sediment
to
ofy–axis
long–shore
sediment
flux
ch links the
speed
displacement
/ dy
> small,
0and
sediment
flux
coastline
tends
∂Qof/ ∂ifshoreline
yflux,
∂(Fig.11b).
Qthe/the
∂the
y increase
Accordingly
the
shoreline
disturbance
is
suppressed
by
the
hcoastline
hat
sediment
and
the
tends
todepth
straighten.
dQ
/ flux
dyis
>results
0 (Fig.11b).
(t angles
isdQthe
time
and
(t∂y–axis
time
directed
and
the
along
the
coast,
directed
isalong
the
water
the
coast,
isthe
the
at t
sediment
flux,
Accordingly
the
shoreline
disturbance
suppre
sediment
flux
and
coastline
tends
tothe
straighten.
Θto
+gradient
δstraighten.
=45
. Hence,
are
along
the
contour
in
growth
There
are
two
limiting
cases,
when
ofwater
wave
approac
∗the
∗angle
=
Θ
lead
to of
the
opposite
situation
(Fig.
10c). depth
An
increase
Large
values
, shoreline
(1),
dQthe
/ the
dyspeed
> speed
0 (Fig.11b).
ingly
the
shoreline
disturbance
is
suppressed
by
the
angle
is flux,
large.
sediment
Accordingly
the
shoreline
disturbance
is
suppressed
by
the
which
links
of
displacement
Θ lea
∂
χ
/
∂
t
Large
values
sediment
flux
and
the
coastline
tends
to
straighten.
to
gradient
of
long–shore
sediment
flux
links
the
of
shoreline
displacement
∂
χ
/
∂
t
sediment
flux
and
the
coastline
tends
to
straighten.
h
sediment
flux
and
the
coastline
tends
to
straighten.
sediment
flux
and
the
coastline
tends
to
straighten.
Figs.
11b
and
11c
show
schematically
the
variations
in
sediment
flux
Q
along
the
shoreline
to
gradient
of
long–shore
sediment
flux
which
links
the
speed
of
shoreline
displacement
∂
t
h
+
z
∂
y
he∂time
and
the
y–axis
is
directed
along
the
coast,
is
the
water
depth
at
the
sediment
flux
and
the
coastline
tends
to
straighten.
∗
∂
Q
/
∂
y
Θ
Θ
+
δ
lead
to
the
opposite
situation
(Fig.
10c).
An
increase
in
along
the
Large
values
∗
c
h
(t gradient
is
the
and
thetends
y–axis
is directed
along
the
coast,
istends
the
water
depth
at
lead
to
the
opposite
situation
(Fig.
An increase
Large
values
flux
and
coastline
to sediment
straighten.
Θ coastline
sediment
flux
and
the
tothe
straighten.
lead
to
the
opposite
situation
(Fig.
10c).
incre
Large
values
∗ Θ
sediment
flux
and
the
coastline
tointhe
straighten.
gradient
of
long–shore
sediment
flux
dQ
/y–axis
dytime
>the
0of
2 tends
sediment
(Fig.11b).
Accordingly
shoreline
disturbance
isalong
suppressed
by
to
gradient
long–shore
flux
∂time
χsediment
/ flux
∂and
tflux,
dQ
dy
010c).
/ ∂χy /(t∂tisto
to
of
long–shore
sediment
flux
displacement
h2 ∗Θ
contour
leads
to
a decrease
sediment
flux,
,words,
and
suchAn
a trend
the
the
directed
along
thethe
coast,
is
the
depth
at
the
Figs.
11b
and
11c
show
schematically
the
variations
in
sediment
Qprofile
the
shoreline
)water
and
close
90º
(to
).
Inis/contour
other
in
the
zto
zsituation
sin
→
0flux
cos
Θalong
→
0at
sediment
and
the
coastline
tends
to
straighten.
is
the
elevation
its
upper
the<(Fig.
elevation
at
its
seaward
border
ofis
the
seaward
active
coastal
border
of
profile
the
active
(closure
coastal
depth)
and
(closure
depth)
and
Θ
lead
toΘ
the
opposite
(Fig.
10c).
An
incrfu
Large
values
clead
csituation
Θ
Θ
Θ
+
δ
leads
to
a
decrea
lead
the
opposite
10c).
An
increa
Large
values
lead
to
the
opposite
situation
(Fig.
10c).
An
increase
in
along
the
Large
values
Θ
Θ
+
δ
Θ
+
δ
lead
to
the
opposite
situation
(Fig.
10c).
An
increase
in
the
Large
values
wave
approach
angles.
According
to
Eq.
(2),
Q
reaches
its
maximum
when
Large
values
to
the
opposite
situation
(Fig.
lead
to
the
opposite
situation
(Fig.
10c)
Large
values
1 for different
∂Q∂∂Qwhich
(t
is
the
time
the
y–axis
isin
along
/ ∂/ y∂flux
dQ
/ values
dy
<∂0tincrease
hleads
Θand
Θawater
+decrease
δthealong
(tlinks
is
the
time
and
the
y–axis
is directed
directed
along
the
coast,
is
the
depth
at
the
lead
to
the
opposite
situation
(Fig.
10c).
An
the
Large
values
dQ
/dQ
dy flux
<dy
0 increase
contour
leads
to
a depth)
decrease
sediment
flux,
,coast,
and
such
athe
trend
favours
sediment
contour
leads
to
ain
decrease
in
sediment
flux,
,<and
such
aΘtrend
Θ
+
δtrefa
to
opposite
situation
(Fig.
10c).
An
in
Large
∂
χ
/
∗lead
/
0
Q
y
h
to
gradient
of
long–shore
sediment
the
speed
of
shoreline
displacement
contour
to
in
sediment
flux,
,
and
such
a
(t
is
the
time
and
the
y–axis
is
directed
along
the
is
water
depth
at
the
z
sediment
and
the
coastline
tends
to
straighten.
is
the
elevation
at
its
upper
r
of
the
active
coastal
profile
(closure
and
=
∗
accretion
and
growth
of
perturbation
amplitude.
cEq.
Θthe
+ δthealong
different
wave
approach
angles.
According
to
(2),
Q
reaches
its An
maximum
when
10c).
increase
in
the
contour
leads
to0and
,Large
(1),
zδcgrowth
Θ
Θ
+the
lead
to
the
opposite
situation
(Fig.
10c).
An
increase
in
along
values
о for
is
the
elevation
at
its
upper
seaward
border
of
the
active
coastal
profile
(closure
depth)
and
h
along
the
coast,
is
the
water
depth
at
the
h
h
is
the
water
depth
at
the
seaward
bor­
d
er
the
coast,
dQ
/
dy
<
sward
ish directed
along
the
coast,
is
the
water
depth
at
the
∗
contour
leads
to
a
decrease
in
sediment
flux,
,
and
such
a
tr
Θ
+
δ
almost
perpendicularly
to
the
coast,
while
in
the
second
case
they
ru
accretion
the
growth
dQ
/
dy
<
0
dQ
/
dy
<
0
=45
.
Hence,
if
the
angles
are
small,
the
increase
in
along
the
contour
results
in
of
dQ
/
dy
<
0
∗
contour
leads
aat
decrease
sediment
tre
contour
leadsleads
toprofile
athe
decrease
inofsediment
flux,
, and
a to
trend
favours
sediment
∗ contour
z,cand
to
agrowth
decrease
sediment
flux,
, such
and
such
a leads
trend
favours
sediment
z c ∂y ofо contour
dQ
/ dysuch
< 0 ,aand
boundary).
boundary).
is
the
elevation
its
the
active
coastal
(closure
depth)
and
contour
to
ain
decrease
in<flux,
sediment
flux,
∗ +border
dQ
/depth)
dy
< 0amplitude.
accretion
and
the
perturbation
a increase
decrease
in
sediment
flux,
,, and
and
such
a, and
leads
to
decrease
in
sediment
flux,
such
aand
trend
sediment
accretion
the
growth
ofupper
the
perturbation
amplitude.
dQ
/ dy
0naturally
contour
leads
to
aTherefore,
decrease
in
sediment
flux,
such
a trend
favours
sed
accretion
and
the
growth
of
the
perturbation
amplitude.
Θofalead
Θ favours
+the
δ
to
the
opposite
situation
(Fig.
10c).
An
in
along
the
Large
values
of
the
active
coastal
profile
(closure
long–shore
sand
waves
can
develop
from
small
z
Θ
+
δ
=45
.
Hence,
if
the
angles
are
small,
the
increase
in
along
the
contour
results
in
growth
of
is
elevation
at
its
upper
seaward
border
the
active
coastal
profile
(closure
depth)
and
c
dQ /profile
dy
<directed
0 , and
∂leads
Q / dQ
∂accretion
yto/border
contour
a(t
in
sediment
flux,
such
a accretion
trend
favours
sediment
hc ∗growth
is> 0the
and
the
y–axis
isshoreline
along
the
coast,
isand
the
depth
at
the
zthe
Therefore,
long–sho
isby
the
elevation
atin
itsEq.
upper
seaward
oftime
the
active
coastal
(closure
depth)
and
trend
favours
sediment
accretion
and
the
growth
of
accretion
and
growth
of
theright
perturbation
amplitude.
dydecrease
sediment
flux,
(Fig.11b).
Accordingly
the
disturbance
is
suppressed
the
boundary).
and
the
ofwater
the
perturbation
amplitude.
and
the
of
the
amplitude.
accretion
and
the
growth
ofperturbation
the
perturbation
amplitude.
The
trigonometric
function
on
the
(2)sediment
can
be expressed
accretion
the
growth
of
the
perturbation
amplitude.
elevation
atgrowth
itslong–shore
upper
boundary).
and
zleads
zTherefore,
sand
waves
can
naturally
develop
from
small
perturbations
of
the
Using
the
CERC
formula
Using
(Coastal
the
CERC
Engineering
formula
(Coastal
Manual,
Engineering
2002),
sediment
Manual,
flux
2002),
Q
is
flux
Q
islap
Therefore,
long–shore
sand
waves
can
naturally
develop
from
small
the
elevation
at
its
upper
sure
and
is
the
elevation
at
its
upper
lndary).
profile
(closure
depth)
and
accretion
and
the
of
the
perturbation
amplitude.
c is the
c growth
∂
χ
/
∂
t
Therefore,
long–shore
sand
waves
can
naturally
develop
from
accretion
and
the
growth
of
the
perturbation
amplitude.
to
gradient
of
long–shore
sediment
flux
ks
thedepth)
speed
of
shoreline
displacement
dQ
/
dy
<
0
coastline
if
the
resulting
energy
flux
deviates
from
the
shore
normal
at asma
contour
to
a
decrease
in
sediment
flux,
,
and
such
a
trend
favours
sediment
the
perturbation
amplitude.
dQ
/ dy >of0formula
sediment
flux,
(Fig.11b).
Accordingly
the shoreline disturbance
is suppressed
by the sand waves can naturally
accretion
and
the
growth
the
perturbation
amplitude.
boundary).
coastline
if
the
resulting
Using
the
CERC
(Coastal
Engineering
Therefore,
long–shore
develop
from
sme
e CERC
formula
(Coastal
Engineering
Manual,
2002),
sediment
flux
Q
is
Therefore,
long–shore
sand
waves
can
naturally
develop
from
sma
Therefore,
long–shore
sand
waves
can
naturally
develop
from
small
perturbations
of
the
Therefore,
long–shore
sand
waves
can
naturally
develop
from
small
perturbations
of
the
sediment
flux
and
the
coastline
tends
to
straighten.
Therefore,
long–shore
sand
waves
can
naturally
develop
coastline
if
theformula
resulting
energy
flux
deviates
from
the
shore
normal
at sediment
athe
large
enough
angle
Using
the
CERC
(Coastal
Engineering
Manual,
2002),
flux
Q
isdevelop
boundary).
coastline
if
the
energy
flux
deviates
from
the
shore
normal
at wher
a at
lara
о resulting
zresulting
Therefore,
long–shore
sand
waves
can
naturally
Therefore,
long–shore
sand
waves
can
naturally
develop
from
small
perturbations
of
the
the
elevation
at
its
upper
seaward
border
of
the
active
coastal
profile
(closure
depth)
and
coastline
the
energy
flux
deviates
from
the
shore
normal
Therefore,
long–shore
sand
can
naturally
from
perturbation
cQ
proportional
to
the
along-shore
proportional
component
to
the
along-shore
of
the
wave
component
energy
flux
of
F,
wave
energy
flux
F,
exceeding
45if
.flux
Such
aiswaves
situation
can
be
observed
under
thesmall
conditions
accretion
and
the
growth
of
the
perturbation
amplitude.
Manual,
2002),
sediment
flux
Q
is
proportional
to
the
Using
the
CERC
formula
(Coastal
Engineering
Manual,
2002),
sediment
is
о
sediment
flux
and
the
coastline
tends
to
straighten.
Therefore,
long–shore
sand
waves
can
naturally
develop
from
small
perturbations
of
the
hdeviates
exceeding
45 normal
.the
Such
aatsit
coastline
ifthe
the
energy
deviates
fromthe
shore
normal
atna
thealong-shore
time Large
and
the
y–axis
isCERC
along
the
coast,
isfrom
the
water
depth
at
the
Using
the
formula
(Coastal
Engineering
Manual,
2002),
sediment
flux
Qangle
isflux
о
coastline
energy
flux
deviates
from
shore
coastline
ifdirected
the
resulting
flux
deviates
the
shore
normal
at
aresulting
enough
develop
from
small
perturbations
of
the
coastline
ifthe
the
Θ
Θ
+aifоcoastline
δnormal
coastline
if
the
resulting
energy
flux
from
the
shore
at
athe
large
enough
angle
lead
to
the
opposite
situation
(Fig.
10c).
An
increase
in
along
the
values
∗observed
if
resulting
energy
fluxunder
deviates
from
shore
о resulting
45
.energy
Such
aenergy
situation
can
be
under
the
conditions
where
winds
blow
oisthe
component
of
the
wave
energy
flux
F,
45
.large
Such
alarge
situation
can
be
observed
the
conditions
where
along-shore
component
of
the
wave
energy
flux
F,
coastline
ifexceeding
the
resulting
flux
deviates
from
the
shore
normal
at
enough
angle
exceeding
45
. Such
a coast
situation
can
be
observed
under
the
w
coastline
ifexceeding
the
resulting
energy
flux
deviates
from
the
shore
normal
at
a conditions
large
enough
proportional
to
the
along-shore
component
of
the
wave
energy
flux
F,
Using
the
CERC
formula
(Coastal
Engineering
Manual,
2002),
sediment
flux
Q
is
predominantly
along
the
and
the
majority
of
energy–carrying
waves
Therefore,
long–shore
sand
waves
can
naturally
develop
from
small
perturbations
of
the
о
astal
Engineering
Manual,
2002),
sediment
flux
Q
is
Q
=
KF
sin(
Θ
+
δ
)
cos(
Q
=
Θ
KF
+
δ
sin(
)
Θ
+
δ
)
cos(
Θ
+
δ
)
boundary).
Θ component
Θ45
lead
opposite
situation
(Fig.
10c).
AnF,
increase
in
along
Large
,energy
,conditions
(2),
(2),
о+ δ
о to the
coastline
if thevalues
resulting
energy
deviates
from
the
shore
normal
at
a conditions
large
enough
angle
оflux
portional
to the
along-shore
ofacomponent
the
wave
flux
ering
Manual,
2002),
sediment
flux
QSuch
issituation
оthe
predominantly
along
the
exceeding
. Such
asituation
situation
canbebe
observed
underthe
theconditions
conditions
w
exceeding
45
.
Such
a
can
observed
under
wh
exceeding
45
.
Such
a
can
be
observed
under
the
where
winds
blow
exceeding
45
.
situation
can
be
observed
under
the
where
winds
blow
о
dQ
/
dy
<
0
proportional
to
the
along-shore
of
the
wave
energy
flux
F,
exceeding
45
.
Such
a
situation
can
be
observed
under
the
con
contour
leads
to
a
decrease
in
sediment
flux,
,
and
such
a
trend
favours
sediment
о
predominantly
along can
the
coast
and
thezexceeding
majority
of
energy–carrying
waves
approach
from
predominantly
along
the
coast
and and
the
majority
of
energy–carrying
waves
a
exceeding
45 .profile
Suchenergy
a situation
be observed
under
the
conditions
where
winds
blow
predominantly
along
the
coast
thethe
majority
of energy–carrying
wav
45
.
Such
a
situation
can
be
observed
under
the
conditions
where
winds
blo
sin(Θ of
+ δthe
)coastline
cos(
Θ
+
δ
)
is
the
elevation
at
its
upper
order
active
coastal
(closure
depth)
and
,
(2),
west.
if
the
resulting
flux
deviates
from
the
shore
normal
at
a
large
enough
angle
о
c
,
(2),
Q
=
KF
sin(
Θ
+
δ
)
cos(
Θ
+
δ
)
proportional
along-shore
component
of
the
wave
energy
flux
F,
, under
(2),
dQ
/ proportionality
dy
<
0majority
exceeding
45
. cos(
Such
ato
situation
can
be observed
the
where
winds
blow
mponent
of
the
wave
flux
F,
contour
toKapredominantly
decrease
in sediment
flux,
,conditions
and
aenergy–carrying
trend
favours
sediment
west.
predominantly
along
the
coast
and
the
majority
ofenergy–carrying
energy–carrying
wa
Using
the
formula
(Coastal
Engineering
Manual,
2002),
sediment
flux
Q
is
predominantly
along
the
coast
and
the
majority
ofmajority
wav
the
coast
the
majority
ofsuch
energy–carrying
waves
approach
from
the
Θ
Θ
Q = accretion
KF
sin(
Θ
+leads
δenergy
Θ
+the
δCERC
along
and
the
of angle
waves
approach
from
the
e wave
energy
flux
F,
where
is
the
proportionality
where
K
isand
constant,
the
constant,
is
the
between
is
direction
the
angle
between
and
the
normal
direction
to
F
theand
the norm
,δalong
(2),
predominantly
along
coast
and
the
of energy–carr
west.
and
the
growth
of
the
perturbation
amplitude.
Q
=)predominantly
sin(
Θ
+) the
) coast
cos(
Θand
+the
δthe
)coast
west.
, majority
(2),
predominantly
along
of
energy–carrying
waves
approach
from
theFthe
о KF
west.
predominantly
along
the
coast
and the
majority
of
energy–carrying
waves
approach
fr
In
the
area
around
Bolshaya
Izhora
village
the
westerly
and
south–w
exceeding
45
.
Such
a
situation
can
be
observed
under
the
conditions
where
winds
blow
Θ
constant,
is
the
angle
between
direction
F
and
the
normal
to
the
predominantly
along
the
coast
and
the
majority
of
energy–carrying
waves
approach
from
the
.) proportionality
In the area around B
Qlong–shore
=thethe
KF
sin(
Θ
+
δperturbation
)around
cos(
Θ
+ component
δamplitude.
) , develop
accretion
and
growth
of the
where
is
the
proportionality
constant,
thethe
Θ
west.
(2),
Θ
west.
west.
where
K
is
proportionality
constant,
is
the
angle
between
direction
F
and
the
normal
to
the
west.
,
(2),
west.
proportional
to
the
along-shore
of
wave
energy
flux
F,
In
the
area
Bolshaya
Izhora
village
the
westerly
and
south–westerly
winds
are
the
Therefore,
sand
waves
can
naturally
from
small
perturbations
of
the
δ
δ
In
the
area
around
Bolshaya
Izhora
village
the
westerly
and
south–we
general
coast
direction,
general
coast
direction,
is
the
angle
of
local
deviation
is
the
angle
of
of
shoreline
local
deviation
contour
of
from
shoreline
its
general
contour
from
its
ge
west.
(2),
Θ
Inapproach
the area
around
westerly
and south
ere K is thepredominantly
proportionality
constant,
isconstant,
thenormal
angle
between
direction
F
and
normal
to normal
the Izhora
Θ energy–carrying
where
K is the
proportionality
is west.
the the
angle
between
direction
Feastern
and
the
to village
the
most
frequent.
Inthe
the
segment
of the
studiedthe
area
the shoreline
turn
along
the coast
the
majority
of
waves
from
theBolshaya
angle
between
direction
Fand
and
the
to
west.
most
frequent.
In
the
easta
Therefore,
long–shore
sand
waves
can
naturally
develop
from
small
perturbations
ofarea
the
In
the
area
around
Bolshaya
Izhora
village
the
westerly
and
south
δ
In
the
area
around
Bolshaya
Izhora
village
the
westerly
and
south–
In
the
area
around
Bolshaya
Izhora
village
the
westerly
and
south–westerly
winds
are
the
direction,
is
the
angle
of
local
deviation
of
shoreline
contour
from
its
general
In
the
area
around
Bolshaya
Izhora
village
the
westerly
and
south–westerly
winds
are
the
g
the
CERC
formula
(Coastal
Engineering
Manual,
2002),
sediment
flux
Q
is
In
the
around
Bolshaya
Izhora
village
the
westerly
most
frequent.
In
the
eastern
segment
of
the
studied
area
the
shoreline
turns
south.
As
a
result,
coastline
if
the
resulting
energy
flux
deviates
from
the
shore
normal
at
a
large
enough
angle
δ
Θ
Θ
general
coast
direction,
is
the
angle
of
local
deviation
of
shoreline
contour
from
its
general
tant,
is the
angle
between
direction
F )and
tothe
the
where
K
is= the
proportionality
constant,
is
the
angle
between
direction
F
and
the
normal
to
most
frequent.
Insupposed
the
eastern
segment
of
the
studied
area
the
shoreline
iscontour
the
angle
of
local
general
coast
In
around
Izhora
village
westerly
and
south–westerly
winds
are
the
Q
KF
sin(
Θ
+ofdirection
δThe
cos(
Θ
+normal
δof
)curvature
most
Inthe
the
eastern
segment
of
the
studied
area
theashoreline
In
the
area
around
Bolshaya
Izhora
village
westerly
and
south–westerly
wints
,local
(2),
δfrequent.
δ sufficiently
the
waves
come
to
coast
under
at
athe
very
large
angle,
while
largeturns
amo
direction
(Fig.
11a).
11a).
The
and
contour
angle
curvature
and
angle
are
to
be
are
supposed
small,
tothe
be
sufficiently
west.
δthe
eeral
angle
between
direction
Fdirection,
and
theδBolshaya
normal
to(Fig.
the
coast
direction,
isarea
the
angle
deviation
ofshore
shoreline
contour
from
its
general
general
coast
direction,
islocal
the
angle
deviation
of
shoreline
contour
from
its
general
In the
area
around
Bolshaya
Izhora
village
theits
westerly
and
south–westerly
winds
are
the
the
waves
come
to the
co
coastline
resulting
energy
flux
deviates
from
the
normal
at
a large
enough
angle
most
frequent.
In
the
eastern
segment
ofthe
thestudied
studied
area
theshoreline
shoreline
о if the
most
frequent.
In
the
eastern
segment
of
area
the
tu
most
frequent.
In
the
eastern
segment
of
the
studied
area
the
shoreline
turns
south.
As
a
result,
deviation
of
shoreline
contour
from
general
most
frequent.
In
the
eastern
segment
of
the
studied
area
the
shoreline
turns
south.
As
a
result,
most
frequent.
In
the
eastern
segment
of
the
studied
area
the
s
the
waves
come
to
the
coast
under
atflux
amost
very
large
angle,
while
a large
amount
of
sand
the
exceeding
45 . Such
a situation
can
be
observed
under
the
conditions
where
winds
blow
δwave
11a).
The
contour
curvature
angle
are
supposed
toarea
sufficiently
small,
nal
to
along-shore
component
of
the
energy
F,be
the
waves
come
tosouth.
the
coast
under
at aon
very
large
angle,
while
aand
large
amou
most
frequent.
In and
the
eastern
segment
of
thethe
studied
the
shoreline
turns
Ascoast
athe
result,
the
waves
come
to
the
under
at
a
very
large
angle,
while
a
large
am
frequent.
In
the
eastern
segment
of
the
studied
area
the
shoreline
turns
south.
As
gle
ofthe
local
deviation
of
shoreline
contour
from
its
general
δ
direction
(Fig.
11a).
The
contour
curvature
and
angle
are
supposed
to
be
sufficiently
small,
δ
general
coast
direction,
is
the
angle
of
local
deviation
of
shoreline
contour
from
its
general
near–shore
provides
a
source
of
material
for
the
development
growth
In
the
area
around
Bolshaya
Izhora
village
westerly
and
south–westerly
winds
are
оIn is
Θ
where
K
the
proportionality
constant,
is
the
angle
between
direction
F
and
the
normal
to
the
direction
(Fig.
11a).
The
contour
curvature
and
angle
δ
11a).
The
contour
curvature
and
angle
are
supposed
to
be
sufficiently
small,
δ
≈
sin
δ
≈
tg
δ
=
∂
χ
δ
/
∂
≈
y
sin
δ
≈
tg
δ
=
∂
χ
/
∂
y
most
frequent.
the
eastern
segment
of
the
studied
area
the
shoreline
turns
south.
As
a
result,
δ
deviation
ofexceeding
shoreline
contour
from
its
general
ection (Fig.
11a).
The
curvature
and
angle
are
supposed
to
be
sufficiently
small,
allowing
to
the
use
of
allowing
approximations
to
the
use
of
approximations
.
.
near–shore
provides
a
sou
45the
. Such
a
situation
can
be
observed
under
the
conditions
where
winds
blow
thewaves
waves
come
thecoast
under
ata under
avery
verylarge
large
angle,
while
alarge
largeam
a
the
come
totothe
at
angle,
while
agrowth
waves
come
tothe
theto
coast
under
atmaterial
a very
large
angle,
while
aprovides
large
amount
ofcoast
sand
oncoast
the
the coast
waves
come
the
coast
under
at aangle,
very
large
angle,
while
a waves
large
amount
ofunder
sand
on
the
the
come
to
the
at
very
large
angle,
near–shore
provides
source
for
the
development
and
growth
structures.
predominantly
along
the
and
majority
energy–carrying
waves
from
near–shore
source
of
material
for
the
development
and
o
the
waves
to
the
coast
a/of∂
very
large
while
a approach
large
amount
ofathe
sand
the
near–shore
provides
a of
source
of
material
for
thea development
and
grow
the the
waves
come
to
the
coast
under
at
aonshoreline
very
large
angle,
while
a large
amount
ofwhile
sand
be
sufficiently
small,
allowing
toshoreline
Θ
+
δdirection
)are
cos(
Θare
+
δcome
)the
δ
≈to
sin
δ
≈
tgatδunder
=avery
χ
yof
δsupposed
,
(2),
urvature
angle
supposed
to
be
sufficiently
small,
most
frequent.
In
eastern
segment
of∂at
the
studied
area
turns
south.
As
athe
result,
eKF
usesin(
of and
approximations
.
δ
(Fig.
11a).
The
contour
curvature
and
angle
are
supposed
to
be
sufficiently
small,
δ
≈
sin
δ
≈
tg
δ
=
∂
χ
/
∂
y
the
waves
come
to
the
coast
under
a
large
angle,
while
a
large
amount
of
sand
on
allowing
to
the
use
of
approximations
.
predominantly
along
the
coast
the
majority
energy–carrying
waves
approach
from
provides
athe
source
material
for(the
thedevelopment
andgrowt
grow
general
coast
direction,
is
the
angle
deviation
shoreline
contour
from
its
general
δare
sin
δlocal
≈
=development
∂cases,
χnear–shore
y of
near–shore
provides
ashoreline
source
ofvery
material
and
near–shore
provides
aδsource
of
material
the
and
growth
of
structures.
near–shore
provides
aThere
of
the
and
growth
of
shoreline
structures.
allowing
toThere
the
of
. near–shore
δwest.
angle
are
supposed
to
beuse
sufficiently
small,
provides
aof
source
offor
material
for
development
the
use
approximations
Θ
Θdevelopment
δand
≈
sin
δsource
≈ tg
δof≈material
=
∂offor
χnear–shore
/limiting
∂for
ytgdevelopment
are
two
limiting
cases,
when
two
the
of/ ∂growth
wave
when
approach
the
angle
offor
approach
iswave
small
isthe
very
(
wing to
the
use
of of
approximations
.δangle
near–shore
provides
a approximations
source
of
material
for
the
development
and
of
shoreline
structures.
provides
a source
of on
material
the
development
and
growth
ofsmall
shoreline
the
waves
come
to
the
coast
under
at
a
very
large
angle,
while
a
large
amount
of
sand
the
δ
≈
sin
δ
≈
tg
δ
=
∂
χ
/
∂
y
near–shore
provides
a
source
of
material
for
the
development
and
growth
of
shoreline
structures.
Θ
se the
constant,
is
the
angle
between
direction
F
and
the
normal
to
the
ons
.
There
are
two
limiting
cases,
when
the
angle
of
wave
Θ
Fig.
11.
(a)
–
definition
sketch;
(b)
and
(c)
–
changes
in
seditwoproportionality
limiting
cases,
when
the
angle
of
wave
approach
is
very
small
(
west.
δ
≈
sin
δ
≈
tg
δ
=
∂
χ
/
∂
y
toare
the
use
ofIzhora
approximations
.Θare
Θ
There
are
two
limiting
cases,
when
angle
of wave
approach
is small
very
small
( small,
δflux
(Fig.
11a).
The
contour
curvature
and
angle
supposed
to
be
sufficiently
In/two
the
area
the
and
south–westerly
winds
the
2around
2village
2 the
2are
There
two
limiting
cases,
when
the
angle
of
wave
approach
isstructures.
very
(the
≈ There
tgδ = are
∂χnear–shore
∂allowing
ydirection
.sin
ment
inshoreline
cases
small
(b)
and
largewaves
(c)the
angles
of case
wave the waves p
Θ
limiting
when
the
angle
of
wave
iswords,
very
(first
and
close
to
90º
) westerly
and
close
to
In
90º
other
( cos
in0 of
).the
In
other
case
words,
in
propagate
first
is cases,
very
small
close
to
approach
Θ→
0Bolshaya
Θ
→
cos
Θwesterly
→approach
0 ).
Θ
→small
provides
a)source
of(sin
material
for(0the
development
and
growth
of
In
the
area
around
Bolshaya
Izhora
village
the
and
south–westerly
winds
are
the
2 angle
Θ
when
the
angle
of
wave
approach
is
very
small
(
δ
approach
to
the
coast.
ast
direction,
is
the
of
local
deviation
of
shoreline
contour
from
its
general
2
2
most
In
the
eastern
segment
of
thecases,
studied
area
the
turns
south.
a result,
and
close
tofrequent.
90º
).close
In
other
words,
in→
the
case
the
waves
propagate
2( cos
2 in
other
words, case
90º
Θ
0 close
Θthe
are
two
limiting
when
the
angle
approach
iswaves
very
small
(propagate
δfirst
≈shoreline
sin
δthe
≈of
tgwords,
δwave
=
χcase
/As
∂the
ythey
)→
and
90º
(the
).
In
other
in
first
case
the case
waves
sinclose
ΘThere
→
090º
cos
Θ
→
0In
)to
and
toto
90º
).first
other
words,
in ∂the
first
case
propagate
allowing
the
use
of
approximations
.in
Θ
→
Θ
0 while
2
2 small
gle
approach
is
( to
almost
perpendicularly
almost
perpendicularly
coast,
the
second
coast,
while
run
second
almost
along
they
therun
shore.
almost along the sh
) and
to0Θ
).( cos
In
other
words,
ininto
the
first
case
the
waves
propagate
Θof
→wave
0
cos
Θ
→
0
most
frequent.
In
the(very
eastern
segment
of
the
studied
area the
shoreline
turns
south.
As athe
result,
waves
come
to the
under
at aangle
very
large
angle,
while a large
amount
of sand on
the
δ are
Fig.
contour
curvature
and
supposed
to be
sufficiently
small,
). to
InThe
other
incoast
the
first
case
thecase
waves
Θ →11a).
0the
2 words,
2 propagate
dicularly
the
coast,
while
in
the
second
they
run
almost
along
the
shore.
almost
perpendicularly
to
the
coast,
while
in the
second
case
they
run
almost
along
the
shore.
)the
andcoast
close
tothe
90º
(on
).while
In
other
words,
in
the
first
case
the
waves
perpendicularly
to
coast,
while
in
the
second
case
they
run
along
the shore.
sinthe
Θcome
→
0to
cos
Θ
→
0function
Θ
There
are
two
limiting
cases,
when
the
angle
of
wave
approach
is very
small
thealmost
waves
under
at
athe
very
large
angle,
a(2)
large
amount
ofin
sand
onalmost
the
20
The
trigonometric
function
The
trigonometric
the
right
in
Eq.
on
can
the
be
right
expressed
Eq.
(2)
in
the
can
first
be expressed
case
as(propagate
in the first case as
other
words,
in
first
the
propagate
ost perpendicularly
to
the
coast,
while
in
case
they
run
almost
along
the
shore.
near–shore
provides
acase
source
of waves
material
for
thesecond
development
and
growth
of shoreline
structures.
,etric
while
in
the
second
case
they
run
almost
along
the
shore.
δ
≈
sin
δ
≈
tg
δ
=
∂
χ
/
∂
y
o thefunction
use of
approximations
.
on
the
right
in
Eq.
(2)
can
be
expressed
in
the
first
case
as
The
trigonometric
function
onthe
thethe
right
Eq.
(2)
canand
begrowth
expressed
in therun
case
near–shore
aand
source
of to
material
for
the2in
development
of shoreline
structures.
2 provides
The
trigonometric
function
on
right
in Eq.
(2)
can
bewords,
expressed
infirst
the
firstascase
almost
coast,
while
in
case
they
almost
alongasthe shore.
close
to
90º
( cos
In second
other
in the
sin
Θperpendicularly
→
0 )the
0 ).the
eight
trigonometric
function
on
right
in
Eq.
(2)
can Θ
be→
expressed
in the
first case
asfirst case the waves propagate
second
case
they
run
almost
along
the
shore.
in
Eq.
(2)
can
be
expressed
in
the
first
case
as
Θ iscan
e are two limiting
cases, when the
angle on
of wave
approach
very
(
The
trigonometric
function
right
in Eq.
(2)
be small
expressed
in the
first case
almost
perpendicularly
to the the
coast,
while
in the
second
case they run
almost
alongasthe shore.
resulting energy flux deviates from the shore normal at According to the data from the State Institution “Saint
a large enough angle exceeding 45о. Such a situation Petersburg Centre for Hydrometeorology and Envican be observed under the conditions where winds ronmental Monitoring with Regional Functions”, in
blow predominantly along the coast and the majority 2000–2004 and in 2007–2009, the frequency of occurrence of westerly and south–westerly, and easterly
of energy–carrying waves approach from the west.
In the area around Bolshaya Izhora village the west- and north–easterly winds was close to the average
erly and south–westerly winds are the most frequent. annual. On the other hand, at Lomonosov settlement
In the eastern segment of the studied area the shoreline (southern coast of the gulf, at the distance of 10 km
turns south. As a result, the waves come to the coast from study area) in 2004 of 18 cases of strong winds
under at a very large angle, while a large amount of there were 8 cases of westerly and south–westerly and
just 2 case easterly wind. In 2005 from 30 stormy
sand on the near–shore provides a source of material for
days 21 wind directions were westerly and 3 days of
the development and growth of shoreline structures.
easterly and north–easterly winds. In 2006 westerly and
The time t needed to form a sand wave of a given south–westerly storms were 5 times more frequent than
The
time
t (5)
needed
to form
a sand
wave
of aofgiven
sizesize
is determined
from
Eq.Eq.
(5) (5)
as as
The
time
t needed
to form
a sand
wave
a given
is determined
from
from
) sinThe
2isΘdetermined
−time
∂χ / ∂tyneeded
nd case as (1 / 2size
. Then
Eq.
(3)
canaas
be
easterly
and north–easterly
storms
toEq.
form
sand wave of a given size
is determined
from Eq. (5)
as (20 cases to 4).
The properties of wave fields are mostly governed
1 1 ⎛ a⎛ ⎞a ⎞
n equation,
by the properties of wind over the entire(6),
fetch
ned from Eq. (5) as 1 ⎛ a t⎞= t = 2 ln2⎜⎜ ln⎜⎜ ⎟⎟ , ⎟⎟ ,
(6),area, that
t = 2 ln⎜⎜ ⎟⎟ , νk νk ⎝ a 0⎝ ⎠a 0 ⎠
(6),over most of the northern
(6), is, by spatial wind patterns
νk ⎝ a 0 ⎠
,
(3),
Baltic Proper and the Gulf of Finland the lack of local
zc
ν for
ν for
(6),
a relatively
small
basin
likelike
the
Gulf
of Finland,
is is
where
thethe
diffusion
coefficient
a
relatively
small
basin
the
Gulf
of Finland,
where
diffusion
coefficient
windlike
and
wave
data
found
from
the
Gulf
ofare
Finland,
is the results of recent
where the diffusion coefficient ν for a relatively small basin
for
a
relatively
small
where
the
diffusion
coefficient
ν
studies
and
reanalyses
of wind
and
properties
in
3
-1 -1
Θ , respectively,
is10
the
d to small and large angles estimated
m32year
(Leont’yev
2005).
The
typical
time
scale
of wave
the
process
is the
to3 be
about
mto2year
(Leont’yev
2005).
The
typical
time
scale
of the
process
is the
estimated
toand
beisabout
10
-1estimated
basin
liketothe
Finland,
be
about
Gulftime
of Finland,
authors.
m2year
(Leont’yev
2005).
Thethe
typical
scale ofundertaken
the processbyis Estonian
the
estimated
be Gulf
aboutof10
Gulf of Finland,
is
103 m2year-1e–folding
(Leont’yev
2005).
The typical
time
scale The amplitude
most important
changes
in regions
adjacent
the
a / aa0/ =
e=it
which
thethe
perturbation
increases
e times.
With
time
te, during
a 0to
e it
during
which
perturbation
amplitude
increases
echanges
times.
With
e–folding
time
te,time
of
the
process
is
the
e–folding
t
,
during
which
study
area
are
connected
with
in
the
directional
scale
of
the
process
is
the
a
/
a
=
e
χ
=
a
sin
ky
λ which
on
of amplitude
and wave
, during
thenumber
perturbation
amplitude increases e times. With
it
e–folding
timea,telength
0
e
the perturbation amplitude increases e times. −With
structure of winds. Namely, during the last 40 years
2 12 −1
ky
tour.
Substitution
intofrom
Eq.
(3)
leads
to
the
.
Taking
a typical
length
of the
observed
sand
waves
as as
follows
Eq.
(6)(6)
that
follows
from
Eq.
that
t
=
ν
k
there
been
significant
increase
in
the
frequency
of
.
Taking
ahas
typical
length
of the
observed
sand
waves
follows
from
Eq.
(6)
that
times.
With a / aof0 χ= =e aititsin
−
1
t
=
ν
k
e
e
a typical
length
of the observed
sand
waves
as of southerly and
follows
from
Eq. (6)
thatoft e the
= νobserved
k 2 . Taking
Taking
a
typical
length
sand
waves
as
south–westerly
winds
and
decrease
e a,
k (=k2=
π 2/ πλ =0.0157)
λ=400 m ( λ=400
easterly
winds the
over
allperiod
of of
Estonia
(Kull
2005).
gives
tee≈4te≈4
years.
Therefore
period
sand
wave
formation
m (m
/ λ =0.0157)
gives
years.
Therefore
the
of sand
wave
formation
λ=400
bserved sand
waves
as
λ =0.0157)
gives
years.
Therefore
theVisually
period ofobserved
sand wave
formation
λ=400
mTherefore
( k = 2π / the
years.
period of
sandte≈4
wave
formation
wave
data
sets
recorded
at
32
3
(4).
times)
is (2-3)t
estimated
as the
time
needed
for for
a one–order
increase
in2 amplitude
(e2–e
e ore 8-12
–e
times)
is
(2-3)t
or 8-12
estimated
as the
time
needed
a one–order
increase
inin
(eBay
Narva–Jõesuu
the
Narva
showed
a
substantial
estimated
as
the
time
needed
for
a
one–order
increase
3 amplitude
estimated
as the 2time
needed for a one–order increase in amplitude (e –e times) is (2-3)te or 8-12
f sand wave
formation
turnsensing
in the predominant
observed wave propagation
in amplitudeyears.
(e –e3This
times)
is (2-3)te orto8-12
years.
This
corresponds
results
of remote
analysis.
years.
This
corresponds the
to the
results
of remote
sensing
analysis. of wave events generated by
3
direction.
The
duration
corresponds
to
the
results
of
remote
sensing
analysis.
years.
corresponds to the results of remote sensing analysis.
–e times) is
(2-3)tThis
e or 8-12
south–westerly
was
longer
in the
comparison
Eq. (5) shows Eq.
theEq.
shorter
is the
length
(5) (5)
shows
theperturbation
shorter
is the
perturbation
length
λ winds
(larger
k), clearly
thethe
faster
is the
growth
of of
(5).
shows
the
shorter
is
the
perturbation
length
λ (larger
k),
faster
is
growth
Eq. (5)k),shows
the shorter
is the perturbation
length λto(larger
k), and
the faster
is the growth
of
northerly
north–westerly
directions
(Raamet et
λ (larger
the faster
is the growth
of the shoreline
the
shoreline
TheThe
is that
the2010).
gradient
of sediment
fluxflux
along
thethe
shorter
the
shoreline
reason
is that
the
gradient
of sediment
along
shorter
al.
The
reason
is disturbance.
thatdisturbance.
thetogradient
ofreason
sediment
moment t=0 anddisturbance.
the signs “−”
and
“+
“ correspond
shoreline
disturbance.
The
reason
is
that
the
gradient
of
sediment
flux
along
the
shorter
he faster isthe
the
growth
of
There is evidence that there is an increase in stormiflux along the
shorter
structure
is
higher
(Fig.
11c).
is higher
(Fig.
11c).
However
Eq.Eq.
(5) (5)
only
describes
processes
with
spatial
andand
structure
is higher
(Fig.
11c).
However
only
processes
with
spatial
. The result (Eq.(5))
means structure
that
the
shoreline
perturbation
ness processes
both
indescribes
the
Baltic
Proper
However
(5)
only
processes
spatial
structure
higher
(Fig.describes
11c). However
Eq.with
(5) only
describes
with
spatial
and (Orviku et al. 2003;
lux along the
shorteris Eq.
scales
exceeding
aexceeding
with
Jaagus
et al.
2008),
and in the
western
part
thelocal
Gulf
ce is small, andand
vicetemporal
versa, ittemporal
will
grow
with
time
ifcertain
the athreshold
scales
exceeding
certain
threshold
with
small
disturbances
smoothed
out
byofby
local
temporal
scales
a certain
threshold
with
small
disturbances
smoothed
out
temporal
scales exceeding
a certain
threshold
with small disturbances
smoothedetoutal.by2008).
local Recent analysis
small
smoothed
out by
local processes.
of Finland (Soomere
es with spatial
and disturbances
Thelength
optimal
sand–wave
probably
is aisresult
of
the
equilibrium
of many
factors
processes.
The
optimal
sand–wave
length
probably
a result
of the
equilibrium
of many
factors
The optimalprocesses.
sand–wave
probably
is a length
result
(Soomere,
2010)
numerical
processes.
The optimal many
sand–wave
length
is a result
of the Räämet
equilibrium
ofand
many
factors simulation of
smoothed
out
local
ofbythe
factors
whichprobably
control the
cally the variations
in equilibrium
sediment fluxof
Q along the
shoreline
wave conditions
forto
1970–2007
also
show
anwill
increase
which
control thethe
regional
coastal
zone
dynamics.
A deviation
one
sideside
or
the
other
leadlead
which
regional
coastal
zone
dynamics.
A deviation
to one
or the
other
will
regional
coastal
zonecontrol
dynamics.
A deviation
to one
in
the
extreme
wave
conditions
in
the
eastern
Gulf of
which
control
the
regional
coastal
zone
dynamics.
A
deviation
to
one
side
or
the
other
will
lead
quilibrium
of
many
factors
ccording to Eq. (2), Q reaches its maximum when Θ + δ
side or the other
lead
decay
of the supporting
mechanisms
Finland.
Such changes may be responsible for a large
to decay
of
the
mechanisms
thisthis
development.
towill
decay
oftothe
mechanisms
supporting
development.
toΘsupporting
decay
oflead
the
mechanisms
+ δwill
this
development.
e increase
along
the
contour
resultssupporting
in growth ofthis development.part of the intensification of coastal processes in the
side
or theinother
TheThe
results
derived
from
thethe
above
simple
model
areare
consistent
with
the2010)
analyses
RSD
results
derived
from
above
simple
model
consistent
the
analyses
of RSD
The results derived
from
the
above
simple
model
Neva
Bay
area
(Ryabchuk
etwith
al.
andofconfirm
The
results
derived
from
the
above
simple
model
are
consistent
with
the
analyses
of
RSD
Accordingly theare
shoreline
disturbance
is
suppressed
by
the
consistent with the analyses of RSD and hydrom- the changes in wind directions traced in the vicinity
andand
hydrometeorological
data. Unfortunately,
there
is aislack
of wind
andand
wave
statistics
for for
thethe
hydrometeorological
Unfortunately,
there
a lack
of wind
wave
statistics
eteorological
there data.
is a there
lack
ofa lack
o straighten.
of Bolshaya
Izhora
village.
and
hydrometeorological
data. Unfortunately,
is
of wind and
wave
statistics for the
with
the analyses
of RSD data. Unfortunately,
wind and wave
statistics
foronly
theonly
study
area.data
The
only
study
area.
The
available
were
published
in ainreference
book
“Climate
of Leningrad”,
study
available
data
were
published
a reference
book
“Climate
of Leningrad”,
Θ + δThe
site situationstudy
(Fig.
10c).
increase
inarea.
along
the
area.
The
only published
available
data
were published
in a reference book “Climate of Leningrad”,
available
data
were
in a reference
book “Clind wave statistics
forAn
the
with
gustgust
speed
published
in 1982.
probability
of occurrence
of strong
(speed
>5 m s—1, —1
, with
speed
published
insediment
1982.
The
probability
of occurrence
of strong
CONCLUSIONS
of Leningrad”,
published
inThe
1982.
The
probability
—1 (speed >5 m s
<mate
0 , and
t flux, dQ / dy
such
a trend
favours
,
with
gust speed
published
in
1982.
The
probability
of
occurrence
of
strong
(speed
>5
m
s
—1
k “Climate of of
Leningrad”,
occurrence of strong (speed
>5
m s
,
with
gust
—1 —1
andand
south–westerly
winds
in study
areaarea
is 31.4%
andand
thethe
exceeding
15 m sm
) westerly
south–westerly
winds
in study
is 31.4%
exceeding
s) westerly
ation amplitude.
speed
exceeding
15) m
s—1) 15
westerly
and
south–westerly
westerly
and south–westerly
winds in study
area isdescribes
31.4% and
the and morphodynamic
15 m s—1
gust
speed
m s—1, withexceeding
This
study
the
litho–
study
areaperturbations
is 31.4%
and
the
for winds
probability
for for
easterly
andprobability
north–easterly
is 13.9%
(Climate
Leningrad,
1982),
so the
probability
easterly
and
north–easterly
winds
is sand
13.9%
(Climate
of
Leningrad,
1982),
so the
s can naturallywinds
developinfrom
small
of the
of
spits
and of
the
genesis
of the
long–shore
probability
for north–easterly
easterly and north–easterly
winds
is 13.9%features
(Climate
of Leningrad,
1982),
so the
easterly
and
winds is 13.9%
(Climate
is 31.4% and
the
sand
waves,
moving
in the direction
ofthree
sediment
flow
eviates from theofshore
normal
at
a largesoenough
angle
frequency
ofthe
winds,
which
long–shore
sand
waves
development
areare
about
times
frequency
offrequency
winds,
which
induce
long–shore
sand
waves
development
about
three
times
Leningrad,
1982),
ofinduce
winds,
which
frequency
of
winds,
which
induce
long–shore
sand
waves
development
are
about
three
times
along
the
southern
coast
of
the
easternmost
part
of
the
Leningrad,
1982),
so
the
long–shore
sand waves
development are about
observed underinduce
the conditions
where
blow
more
thanwinds
thethe
frequency
of winds,
thatthat
cause
suppression
ofinshoreline
disturbances.
Over
thethe
lastlast
more
than
frequency
of
winds,
cause
suppression
of
shoreline
disturbances.
Over
Gulf
of
Finland
vicinity
Bolshaya
Izhora
village.
threethan
times
more
than of
thewinds,
frequency
of winds,
that of shoreline disturbances. Over the last
more
the
frequency
that
cause
suppression
ntmajority
are about
three
times
of energy–carrying
waves approach
from the
The predominant
direction
of long–shore
sediment
cause suppression
of wave–like
shoreline
disturbances.
Over
decade
wave–like
shoreline
contours
were
observed
for for
thethe
firstfirst
time
in 2004
andand
thethe
long–shore
decade
shoreline
contours
were
observed
time
in 2004
long–shore
flow
is
to
the
east.
Surface
sediments
in
the
near–shore
decade
wave–like
shoreline
contours
were
observed
for
the
first
time
in
2004
and
the
long–shore
the
last
decade
wave–like
shoreline
contours
were
disturbances. Over the last
waves
have
become
evident
in 2006–2007.
According
to the
datadata
from
thethe
State
of study
area
are represented
by
sands
of
different
sand
waves
become
evident
inzone
2006–2007.
According
to the
from
State
observed forsand
the
first
time
inhave
2004
andmore
themore
long–shore
waves
to characteristics,
the data from the
State and origin. Along
ra
villageand
thesand
westerly
andhave
south–westerly
winds
are the in
n 2004
the
long–shore
grain–size
thickness
sand
waves
havebecome
becomemore
moreevident
evident
in 2006–2007.
2006–2007. According
Institution
“Saint
Petersburg
Centre
for for
Hydrometeorology
andand
Environmental
Monitoring
with
Institution
“Saint
Petersburg
Centre
Hydrometeorology
Environmental
Monitoring
with
of
area
the shoreline
south. As
a result,
“Saintturns
Petersburg
Centre
for Hydrometeorology and Environmental Monitoring with
e the
datastudied
fromInstitution
the State
Regional
Functions”,
2000–2004
andand
in 2007–2009,
thethe
frequency
of occurrence
of westerly
Regional
Functions”,
in 2000–2004
in 2007–2009,
frequency
of occurrence
of westerly
21
very large angle,
whileFunctions”,
a large
amount
sand
on theinand
Regional
inof2000–2004
in 2007–2009, the frequency of occurrence of westerly
onmental Monitoring
with
andand
south–westerly,
andand
easterly
andand
north–easterly
winds
waswas
close
to the
average
annual.
OnOn
south–westerly,
easterly
north–easterly
winds
close
to the
average
annual.
al for the development and growth
of
shoreline structures.
andofsouth–westerly,
and easterly and north–easterly winds was close to the average annual. On
of occurrence
westerly
thethe
other
hand,
at Lomonosov
settlement
(southern
coast
of the
gulf,
at the
distance
of 10
kmkm
other
hand,
at Lomonosov
settlement
(southern
coast
of the
gulf,
at the
distance
of 10
( )
( () )
the shore there is up to 2 km long accretion terrace,
seawards from which the depth increases relatively
fast. There are two sources of material for sand spit
formation – erosion of the submarine sand terrace and
erosion of sandy coastal cliffs up–drift of the accretion area.
The coastal segment in front of Bolshaya Izhora
village has complicated dynamics with long–term
development of sand spits some hundreds meters
long and some tens of meters wide. In the vicinity
of Bolshaya Izhora village the maximal width of the
area of relict sand spits and lagoons reaches about 500
m. The spits have separated from the open sea; small
narrow lagoons are gradually becoming shallower and
overgrowing with water plants. Radiocarbon dating
shows sand spit formation has occurred for at least
the last 2500 years. Long-shore sand waves occur
along the seaward edge of the contemporary marine
sand spit. An important feature of the observed sand
cusps is an increase in size (both length and amplitude)
in the eastern direction. The amplitude of the cusps
grows to the east from 15 m to 100 m with down–drift
strait shoreline segments from 100 m (in the west) to
900 m (in the east) long. The sand cusps migrate in
an eastern direction with an average rate from 15 to
20 m year-1.
The reason of the long–shore sand wave’s development is explained by the fact that prevailing waves
induced by the westerly winds propagate almost parallel to the shore. In this case the shoreline contours are
unstable and small perturbations tend to grow over
the time. If the sand volume in the near–shore zone is
large enough, these perturbations can transform into
sand “waves”, migrating in the direction of sediment
flux. The size of sand waves in the Eastern Gulf of
Finland matches the size of similar structures on the
Atlantic coast of Long Island (Thevenot, Kraus, 1995).
However, in the latter case of high–energy coastal environment both the long-shore sediment flux and the
migration speed are ten times greater.
A possible reason for the recent development of
sand waves within study area may be the increase in
the frequency of south–westerly winds and decrease in
southerly and easterly winds established for adjacent
western part of the Gulf of Finland (Kull 2005).
Acknowledgements
The research was funded by the Committee of Nature
Use, Environmental Protection and Ecological Safety
of Saint Petersburg City Government, Federal Goal–
Oriented Program “World Ocean” and grants from the
Russian Foundation for Basic Research 08–05–00860,
09–05–00034–а and 09–05–00303–а. We are very
grateful to Mikhail Spiridonov, Svyatoslav Manuilov
and Yury Kropatchev for their assistance, joint field
work and fruitful discussions. We address our cordial
thanks to Prof. Kevin Parnell (James Cook University,
22
North Queensland, Australia) for revising English of
article and important comments. Valuable remarks
of the reviewers Prof. Tarmo Soomere and Dr. Boris
Chubarenko are appreciated very much.
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