I n t e r n a t i o n a l H y d r o g r a p h i e R e v i e w , M on aco , L I V (1)
J a n u a r y 1977.
CONSIDERATION OF METEOROLOGICAL CONDITIONS
WHEN DETERMINING THE NAVIGATIONAL WATER
DEPTH OVER A SANDWAVE FIELD
b y D.N. Lanc, h o r n e
In stitu te o f O c e a n o g ra p h ic Sciences, T a u n t o n , U K
A m o d i f i e d v e r s io n o f a p ap er p res e n ted at the 15th A n n u a l C a n a d ia n H y d r o g r a p h i c
Co n fe re n c e , O t t a w a , A p r i l 1976, re pr od u c e d w i t h p e r m is s io n o f th e D o m i n i o n H y d r o gr:i pher.
ABSTRACT
In a sa n d w a v e fie ld in the O u ter T h a m e s E stu a ry, G reat Britain , dune
bed f o r m s o ccu r on the fla n k s and crests o f the sa n dw aves. Studies o f the
dunes, as dep icted by h igh -reso lu tion sonar, show that the dunes are
n o r m a lly d o m in a te d by tidal f l o w co n d itio n s and that a r e l a t i v e l y constant
mean w a v e length (4.5 in) is m a in ta in ed . In the event o f a dverse wreather
w h e n large su rface w a v e s occur in the area, the tidal dunes are re p la ced b y
dunes w it h a s ig n ific a n t ly shorter w a v e length (1.5 m to 1.7 m ) . W i t h the
m o d era tio n o f w a v e cond ition s the du nes p r o g r e s s iv e ly r e v e r t to their tida l
eq u ilib riu m condition .
I f such re d istrib u tio n o f sedim ents can be sh ow n to o ccu r on the fla n k s
o f a sandw ave, then s im ila r or g r ea ter action is to he e x p e c te d in the crestal
area, p rob a b ly a ffe c tin g safe n a v ig a tio n a l depths.
INTRODUCTION
Studies o f sa n d w a v e s have been c a rr ie d out in the tida l m a rin e e n v ir o n ­
m ent f o r over 100 years. Up until th e 1930s, w h e n the echo sou nder w a s
developed, m ost o f the studies w e r e re stricted to o b serva tio n s in s h a llo w
water, o r in areas e x p o sed at lo w tid e ( C o r n i s h , 1901). W i t h the in tr o d u c ­
tion and c o m m o n usage o f the echo sounder, and later o f sidescan sonar,
it becam e possible to delineate o ffs h o r e sa n dw ave fie ld s and a tte m p t
cla ssifica tion based upon m o r p h o l o g y (V a n V e e n , 1935). M u ch o f the
interest in sa n d w a v e s in the 1950s a n d early 1960s w a s directed to w a r d s
m a p p i n g the areas o f occu rren ce a n d d efin in g directions o f net sediment
transport based upon cross sectional as y m m e tr y ( S t r i d e , 1959).
Attem pts
w ere m ade to m eas u re lateral m ovem ent o f indiv idua l s a n d w a v es, but in
m a ny cases the results w e r e a m b i g u o u s as possible movem ent, m e a su re d
over a com pa ra tiv ely short tim e scale, w a s less than the ac c u ra c y o f the
position fixing system b e in g used ( L a n g e r a a r , 1966).
D u r i n g the late 1960s
sa n d w a ves becam e of considerable importance to the m a r in e r o w i n g to the
rapid increase in size o f b u l k carriers a n d the associated r e q u ire m e n t to
navigate w ith a m in im u m o f u n d e rk e el clearance ( D i c k s o n , 1967).
B y 1970
it w a s c o m m o n practice fo r deep d r a u g h t tankers, d r a w i n g u p to 14.8 m, to
reach the oil term in als o f the P o rt of L o n d o n h av in g experienced u n d e rk e el
clearances o f a p p r o x i m a t e ly 1 m ( W h i t e ,
A t
1
T ~
~ „
-J
FJ
J
HV/dU)
n , ^
U 1L
^ U lll I
U1
1972).
^
4 -».-.
t lill J
T 'l
lu
It
/>1, ________ 1
_ .v .*
l_
'willL/ll
is the m ain approach route into the T h a m es E stu a ry and the P o r t o f
London , there is a sa n dw ave field w hich reduces the n aviga tion a l w a te r
depths o f that area to 13 m b elo w Ordnance Datum, a redu ction o f
a p p rox im a tely 36 % (fig. 1).
Research has been carried out in the area
since 1969 ( L a n g h o r x e , 1973), p r im a r ily on account o f its im p o r ta n c e to
the P o rt f o r the n avigation o f deep drau ght vessels. Up until 1967, B la ck
Deep Channel rem ained w it h o u t navigational buoys and o n ly p o o r ly sur­
veyed. T h e precedin g h y d r o g ra p h ic s u rv ey o f 1951 did not establish the
existence o f the sandw ave field , as the echo sounding traverses had been
orientated a p p r o x im a te ly pa ra llel to the sandw ave crest lines. A t this tim e
I'M.. 1. — L o c a tio n d iagra m .
it w a s s u r v e y p r a c tic e to ru n s u r v e y lines across a c h a n n e l so th a t the
bo u n d a ries m a y be m o r e a ccu ra tely delin eated.
F o r the p u rp ose o f this p a p er an a r b i t r a r y d iv is io n has been m a d e
betw een s a n d w a v e s a nd dunes, based u po n size. T h e t e r m s a n d w a v e is used
to r e fe r to the la rg e r h y t h m i c fea tu res w h i c h are r e a d i l y d etec te d b y echo
sounding, w h il s t dunes are the sm a lle r fe atu res, w i t h w a v e len gth s o f up
to 15 m, w h i c h o ccu r f o r m e d in the su rfa c e sedim ents.
THE LO N G SA N D HEAD SA ND W AV E FIELD
T h e sa n d w a v e s w it h i n the fie l d at L o n g s a n d H e a d a re e lo n g a te d
d e p o s itio n a l rid ges o f n on -co h es ive sed im en t, o rien ta ted w it h sinuoxis crest
lines a p p r o x i m a t e l y at rig h t angles to the d o m in a n t tid a l f l o w d irection s.
M a x i m u m s a n d w a v e h e ig h ts reach 7.3 m. In d iffe re n t a rea s o f the fie l d t h e y
m a y be s y m m e t r i c a l o r a s y m m e t r ic a l in cross-sectional p r o file , w it h lee
slopes f a c i n g b o th in to and a w a y f r o m the flo o d tide. L e e slopes, o r
m a x i m u m slopes in the case o f s y m m e t r ic a l sa n dw aves, do n o t a p p r o x im a t e
to the a n g le o f rep os e o f sed im en t in w a t e r (28"- 3 2°). M e a n lee-slope a ngles
b e tw e e n crest and tro u g h m easu red f r o m sca le-c orrected echo sou nder
re cord s e x c e p t i o n a ll y re a c h 15” , w h il s t the a ver a g e slope f r o m som e 110
m e a s u r e m e n ts is 8.4". T h e sa n d w a v e s are r e la t iv e ly stable features, and
in d ivid u a ls m a y be re c o g n is e d b y th e ir f o r m and p o s itio n f r o m 1967 u ntil
the presen t d a y (1976). L a t e r a l m o v e m e n t o f the gross s a n d w a v e f o r m s
re m a in s a m b ig u o u s since m e as u red valu es a re not s ig n ific a n t r e la t iv e to
the a c c u ra c y o f the D ecca H i - F i x p o sition f i x i n g sy s te m w h i c h has been
used th r o u g h o u t the studies.
T h e po sitio n o f the sa n d w a v es in re la t io n to the n e i g h b o u r in g b a n k s and
coastline is such that lo n g u n im p e d e d w a v e fetch o n l y re ac h es the area
f r o m the n orth east. F r o m this d ir e c t io n o ccasional, bu t severe, g a le - fo r c e
w in d s occur. It is a lso th e d ir ectio n a p p r o x i m a t e l y p a r a lle l to the f l o o d tide.
D u n e bed f o r m s , w h i c h are se c o n d a ry in size to the m a j o r sa n d w a v e,
are c o m m o n t h r o u g h o u t the s a n d w a v e fi e ld and also in e x te n s iv e a reas o f
r e l a t i v e ly level sea bed to the south o f the fie ld in B la c k D e e p Channel. T h e
dunes, w it h w a v e le n g t h o f up to 15 m and h eig h t o f up to 1.0 m, a re n ot
re a d ily detected b y ech o so u n din g as th e ir h e ig h t is c o m p a r a b l e w i t h that
o f u n r e c o rd e d s h ip ’ s m o t io n . In no case, h o w e v e r , h a v e sidescan sonar
records r e v e a le d s a n d w a v e s w h ic h a re fr e e f r o m dunes. M e a s u r e m e n t s m a d e
fr o m sca le-c orrected sonar records s h o w that, th o u g h the du nes are
n o r m a ll y o r ie n ta te d p a ra lle l to the s a n d w a v e crest lines, ex c e p tio n s are
c o m m o n ; and d iv e r g e n t angles o f up to 8 0 “ have been re co r d ed . T h e r e is
a t en d en cy f o r du nes to decrease in size clo se to the crests o f the sa n dw aves,
p r o b a b ly in a sso cia tion w it h the h ig h shear stresses wTh ic h o ccu r in this
area on b o th flo o d and ebb tides. U n d e r tida l co nd itio n s, there does not
appear to be a n y o th e r o b vio u s r e la tio n s h ip betw een d u n e size a n d po sitio n
on the fla n k o f a s a n d w a v e ( fig . 2). F i g u r e 3 sh ow s th a t t h o u g h the du n e
size o fte n decrea se clo se to the s a n d w a v e C r e s t l i n e , e x c e p t io n s a re not
unusual. C l o e t ( p e r s o n a l c o m m u n i c a t i o n ) , c a r r y in g o u t clo se-lin e (13.5 m )
T
77 metres
Fic. 2. —
Fir.. 3. —
Side sca n
s o n a r re co rd
s h o w i n g d un es in t id a l
o f a sandwave.
e qu ilib riu m
on
th e f la n k
E ch o s o u n d e r re co rd s h o w i n g th e o cc u rre n c e o f d un es on s an dw av es .
echo so u n din g traverses across sa n dw aves in (he Sandettie area shows that
h eigh t u ndulatio ns on in d ivid u a l sa n d w a v e crests m a y reach 1.4 in. T h o u g h
these m a y not be d ir e c t ly attrib uted to the presence o f dunes on the
crestlines, they do indicate that such va ria tio n s in sa n d w av e heigh t are to
be expected.
D iv e r observation s reveal that dunes, u nlik e the large-scale sandw aves
in the L o n g sa n d Head area, m a in ta in lee slopes w h ic h are close to the
angle o f repose o f sedim ent in w a te r. Slight disturbance causes these slopes
to avalanche.
It is considered that the steepness o f slope o f a sa n d w av e or dune is
im p orta n t in that it is indicative o f the re lative a c tiv ity o f the feature. In
those cases w h e r e the su rfa c e o f a s a n d w a v e is c o m p le t e ly ca rp eted in dunes,
a n y change in f o r m or ch a nge in p o sition o f the gross s a n d w a v e w i l l be
the resu ltant o f the ch anges w h ic h h a v e o ccu rred in the dunes, o r sedim en t
passing t h r o u g h the dune re g im e . In a greem e n t w it h A l l e n & C o l l i n s o n
(1974) it is accepted that at a n y one t im e there is o n ly one a c t iv e bed fo rm ,
though m o r p h o l o g ic a l l y t w o or m o r e m a y be id en tified .
DUNE STUDY AREA
In o r d e r to stu d y the tem p o r a l sta b ility o f dune bed fo r m s , an area
w i t h i n the s a n d w a v e f i e ld w a s selected f o r detailed o b serva tio n s. T h e
selected area la y on the stoss slope o f a sa n d w a v e o f so m e 4 m in height,
the w a te r depth above the crests b e in g a p p r o x i m a t e l y 12 m . A sedim ent
sa m p lin g p r o g r a m m e in d ica ted that the m e a n g r a in size o f the sed im en t in
this area ran ges f r o m 1.25 <f> to 0.75
(m e d iu m to coarse sand, 425-600
m ic ro n s ).
FIELD D ATA
Sidescan Sonar
EG&G D u a l Channel sidescan so n a r (fr e q u e n c y 110 k H z , pulse length
0.1 m s) w a s used e x t e n s iv e ly to m a p the r e la tiv e distrib u tio n a n d c o n f i g u r a ­
tion o f the dunes in the research area.
In o r d e r to obtain re p e t it iv e sonar co ver o f the sa m e a rea o f the sea
bed the P o r t o f L o n d o n A u t h o r i t y H i - F i x Chain w a s used f o r position
control. U s in g this sy stem it w a s estim ated that the sa m e sh ip’ s tra c k could
be n aviga ted to a re p ea tab le accu ra cy o f better than 10 m ( L a n g h o r n e &
H o o p e r , 1974). T h is a ccu ra cy w a s a ccep ta ble in co n s id era tio n o f the dual
channel sonar ra n ge o f 154 m (500 f t ) w h ic h w a s used. O n w e l l co n trolled
tracks, in go o d sea cond ition s, the h ig h -reso lu tio n sonar g a ve records o f
su ffic ien tly h igh q u a lit y that in d iv id u a l dunes could be p o s i t i v e l y id e n t ifie d
f r o m one tra verse to the next. M o r p h o lo g ic a lly , dune re c o g n it io n is m a de
possible b y their in d iv id u a l f o r m ch aracteristics and in te rre la t io n s h ip w it h
n e ig h b o u r in g dunes ( fig . 2).
A c c u ra te m e a s u rem e n ts o f dune w a v e len gth can o n l y be o btain ed f r o m
sonar records if co rrection s are m a d e f o r slant ra n ge and sh ip’ s speed o ver
the grou n d ( F l e m m i n g , 1976). H a v in g a pplied these c o rrection s, statistical
values o f du n e w a v e len gth w e r e obtain ed b y both Q u a n t im e t Im a g e
A n a ly s e r <*' and m a n u a l methods.
Wave Recording
F r o m 1973 o n w a r d s w a v e data w a s m a d e available b y the P o r t o f
L o n d o n A u th o r it y . D u r i n g this p e r io d w a v e r e c o r d in g w a s ca rr ied out on
(*) I m a g e A n a l y s i n g C o m p u t e r s Ltd., M e lb o u r n , R o v s t o n , H e rt s ,
E n g la n d .
Sunk n a v ig a tio n b u oy 4.5 km fr o m the research area. A standard W a v e r i d e r
sensor ( * ) w a s installe d on the buoy ( f o r sa fety from passin g sh ippin g) and
the w a v e data was tra n sm itted via W a l t o n P ie r to the P o r t control at
Gravesend. Calib ratio n w as necessary in order to obtain accurate data f r o m
the response o f the n a v iga tio n buoy. A ccep ta ble results w e re obtained f r o m
w a ves o f la rg er a m p litu d e and period, w h ic h are the w a ves w hich have
s ig n ific a n t effect on the sea bed at 12 m depth.
T o obtain an in dica tion o f the possible effect o f w a v e action at the sea
bed, an a p p rox im a te particle oscillation velocity at a giv en dep th can be
calculated usin g A i r y ’ s (1845) equation :
in w h ic h
T
k
h
L
H
=
=
=
=
=
w a v e period
wTave num ber = 2 7t/L
w a te r depth
surface w a v e length
w a v e h eigh t (crest-to-trou gh )
m a x im u m oscillation v e lo c ity at the sea bed
In o rd e r to m a k e a q u an titative com parison o f the differen t periods o f
adverse w ea ther, o scillatio n velocities at the sea bed are calculated using
valu es o f sig n ific an t w a v e height (m ean height o f highest one third o f
re co rd ed w a v e s ) and c o rresp o n d in g p eriod obtained f r o m the analogue w a v e
records. ( T o get m o re accurate results spectral m eth ods must be used
( H a d l e y , 1964), but f o r the present purposes the basic m e th o d used here
gives adequ ate results).
T idal F low
T id a i f l o w data w a s recorded o v e r an 18-day p eriod at a h eigh t o f one
m e tr e above the sea bed, in a position in the trough betw een the sandwaves,
u sing a b o tto m -m ou n ted s elf-reco rd in g current meter. A s u m m a ry o f the
analysis o f the data is show n in fig u re 4. T a k in g a critic al erosion velo city
(at 1 m ) o f 30 c m r 1 f o r coarse sand (0.5 <£) ( S o u l s b y (in p res s) a fte r S h i e l d s
(193 6 )), assu m in g a lo g a rith m ic v e lo c ity p r o file and a ro ughness length o f
0.25 cms, the flo o d tide exceeds the critical velo city f o r 38% o f the period
o f a tidal cycle, w h ils t the ebb tide o n ly exceeds the critical v e lo c ity fo r
26 % o f the p eiio d. B o th m a x im u m flo o d and ebb \elocities rcacli 60 cms
but in each case fo r less than 1 % o f the period.
Grain Size Distribution
T h e grain size d istrib u tio n w ith in the sandwave fie ld w as obtained by
sieve analysis (0.25 ¢) in terva l o f sieve sizes) o f sediment samples obtained
b y both gra b sam p lin g and vibrocoring.
(*) D a t a w e l l
N e th e rla n d s .
b.v.
L ab oratorium
voor
in s t r u m e n ta tie ,
Zoom erlu ststra at
i,
H a a rle m ,
Fit;. 4. — T i d a l f l o w data. R e c o r d e d o v e r ail 18-day p e r i o d a t a h e i g h t o f 1 m e t r e a b o v e
the sea bed, in a p o s i t i o n in th e t r o u g h b e t w e e n s a n d w a v e s .
A N A LY S IS OF FIELD D A T A
D u r in g the period 1971 to 1974 sidescan sonar data w a s o b ta in ed o v e r
a sta n d ard track w h ic h w a s o rien ta ted a p p r o x i m a t e ly p a r a lle l to the du n e
crest lines in the stu dy area. T h e m a j o r i t y o f sonar re co r d s s h o w e d a r e la ­
t i v e ly co n s ta n t dune p a t t e r n w it h a m e a n w a v e len gth o f 4.5 m ± 0.3 m.
R e p e t i t i v e ob serva tio n s o v e r a t w o -d a y p e r io d f a ile d to s h o w a n y in d ic a tio n
o f re vers al o f a s y m m e t r y d u r in g the course o f successive fl o o d a n d ebb tides.
R e c o r d s ob tain ed o v e r a s ix - d a y period, fr e e f r o m a d v e r s e w e a t h e r (i.e.
ca lcu la ted w a v e - in d u c e d o scilla tio n v elo cities at 12 in depth n e v e r ex ceed ed
14 c m s ' 1) s h o w ed that in d iv id u a l dunes m a in t a in e d their i d e n t i t y o v e r such
periods. O v e r a lo n g er t im e scale, J u ly to O c t o b e r 1971, the c a lcu la ted m e a n
w a v e len gth ch a n g ed f r o m 4.5 m to 4.2 m (sta n d ard d e v ia t io n 1.8 m a nd
1.5 m re s p e c t iv e ly ) bu t it w a s n ot possible to id e n tify , w i t h c o n fid en ce, a n y
in d iv id u a l du n e f r o m o ne s u r v e y to the next. D u r in g this p e r io d no w a v e
data w a s a v a ila b le but m e te o r o lo g ic a l data suggested that e ffective w a v e
action w a s p r o b a b ly o f m i n o r im p o r ta n c e as w i n d speeds n e v e r ex ceed ed
25 kn ots w h e n b l o w i n g f r o m the N o r t h o r East, the d ir e c t io n s o f lo n g
w a v e fetch.
D u r i n g the p e r io d o f study, th ree sequences o f o b s e r v a tio n s
o b tain ed w h ic h r e q u ir e m o r e deta iled description, n a m e ly :
w ere
March 1972
In M a rc h 1972 sonar o b ser va tio n s in th e resea rch a re a h a d to b e
d ela y ed on account o f a d v e r s e w ea th er . M e t e o r o lo g ic a l o b serva tio n s at
S h o eb u ryn ess re c o r d e d m ean w in d speeds o f in excess o f 20 knots f o r a
p eriod o f 71 h ou rs f r o m a d ir e c tio n o f b e t w e e n 060" and 100“ (s u r fa c e w a v e
letch 120 to 65 m ile s ). S i m i l a r co n d itio n s w e r e r e c o r d e d at G a llo p e r and
S h ip w a sh ligh t vessels.
I he o n l y s o n a r data a v a ila b le w a s o b tain ed so m e
c lim a x o f the ga le (g a le m a x . + 123 h o u rs ) (fig . 5). T h e
(he tidal c u rr e n t d u n e p a tte rn n o r m a l l y associated w it h
c o m p le t e l y re p la c e d b y a p a ttern o f du n es w it h s im i la r
c o n s id e r a b ly sh o r te r w a v e length.
5 days a ft e r the
re c o r d sh ow s that
the area had been
o rie n t a t io n but o f
A n a l y s is o f du n e w a v e le n g th f r o m f ig u r e 5 s h o w s that w it h in crease
in w a t e r d ep th th ere is a te n d e n c y f o r a d ecrea se in du n e w a v e length.
C alcu lated m e a n w a v e len gth in the n ea r-crest z on e =
C a lcu la ted m e a n w'ave len gth at m id - s lo p e
=
Calcu lated m ean w a v e le n g th in the t ro u g h
=
T h i s c o n c lu s io n su ppo rts the fi n d in g s o f I n m a n (1957), H
K o m a r (1974) f o r w a v e - g e n e r a t e d dunes.
3.1 m
2.6 m
1 . 7 ni
arm s
(1968) and
M a y 1973
R e p e a t so n a r s u rv e y s w e r e p la n n ed on a d a i ly basis b e tw e e n 8 and 20
1973. O n 16 and 17 M a y, sea c o n d itio n s p r e v e n t e d observation s.
lug this p e r io d m e t e o r o l o g i c a l o b s e r v a tio n s at S ho eb u ryn ess r e c o r d e d
m e a n w i n d speeds o f in excess o f 20 kn ots f o r a p e r io d o f 36 hou rs f r o m
a d ir e c t io n o f b e t w e e n 060" and 90" (s u r fa c e fetch 120 to 80 m iles).
May
W a v e r e c o r d s o b tain ed at Sunk B u o y s h o w e d that the m a x im u m w a v e
î e ig h l re a c h ed 2.90 m w h ils t the sig n ific a n t w a v e h eigh t reac h ed 1 8 0 m
w it h a c o r r e s p o n d i n g p e r io d o f 5.56 seconds. U sin g va lu es o f sig n ific a n t
w a v e h e ig h t and p e r io d w it h the e q u a tio n g iv en , the m a x i m u m calcu lated
o s c illa tio n v e l o c i t y at the sea bed (12 m ) re a c h ed 3 9 c m s - i and r e m a in e d
in excess ol 2 6 c m s - ' f o r a p eriod o f 16 hours. T h e s e ca lcu la ted velo cities
occurred superimposed upon a tidal flo w
stated, can reach 6 0 c m s ~ '.
velo city which, as previously
Oscillation velocities derived from w ave records obtained for the
re m ainder o f the survey period on no occasion exceeded 14cm s 1 at 12 m
water depth and therefo re w ere o f little significance in terms o f sediment
movement.
By comparison o f sonar records, individual dunes could be identified
over the six day period prior to the adverse weather. T h e mean w ave length
remained relatively constant and comparable w ith records obtained on other
occasions. (Mean w avelength 4.5 m ± 0.2 m ). Sonar records obtained in
poor sea conditions on 18 May, the first opportu nity after the adverse
weather, revealed the presence o f short w a ve length dunes ( < 1 m) super­
imposed upon the larger tidal dunes, with some suggestion o f the latter
fo rm in g double crests. Records obtained two days later confirm ed the
form ation o f double crests whilst no evidence remained o f the presence o f
short w a ve length dunes (fig. (>).
F ig .
6. —
Sidescan sona r record s h o w in g ti d al dunes p a r t ly m o d i f i e d by surface
w a v e action.
Dune comparison — Post gale sequence
A fu rth er sequence o f sonar data was obtained in October and
N o v e m b e r 1974. On 16 October it w as established that the tidal dune
configu ration was present. A d verse w eather occurred 22-24 October, and
again 29-30 October. T h e magnitude o f the gales and the resulting w ave
conditions are summarised in T a b le 1.
T h e first o f a series o f post-gale sonar surveys was conducted on
31 October 2nd gale max. + 35 hours). A n a ly sis o f the data showed that,
as is the case w ith the March 1972 data, the tidal dunes had been replaced
by short-wave-length w ave-induced dunes (X crest = 1.72 m, A. mid-slope
= 1.67 ni, X trough = 1.55 m ). Six fu rth er sonar surveys were carried out
term inatin g on 7 N o v e m b e r (2nd gale max. + 203 hours). During this
period the sonar records showed an increase in dune w a ve length o f up to
a p p rox im a tely 70% (trou gh ) to 80% (crest) o f the normal equilibrium tidaldune w a v e length.
T
able
I
29 - 30 O c t o b c r
22 - 24 O c t o b e r
Wi nd :
Di recti on
330-040°
270 - 33 0°
Fe t c h
10 - 4 5 0 N Miles
9 - 11 N Miles
Mean speed
> 20 Kt s f o r 24 hours
> 20 Kt s f o r 4 4 hours
0.8 - 2.8 m
1 .2 - 2.0 m
Waves :
Si gni f icant wave
height
Perimi
3 7 - 6 1 see
3 .8 - 5 .4 sec
Osci l l ati on ve l o c i t y
> 25 cnis~ 1 f or
> 2 5 c m s ' 1 f or
21 hours
34 hours
(at 12 m )
> 3 5 cms
> 3 5 cms
1 f or
1 f or
4 hours.
27 hours
DISCUSSION
T h e fie ld data o b ta in e d in dicates that, in the p a r t i c u la r area w i t h i n the
s a n d w a v e fie ld at L o n g s a n d H ead, the dune r e g im e is c o n t r o lle d by bo th the
(id a l f l o w and w a v e co n d itio n s. M o s t o f the data in dica tes that the tidal
du n e r e g i m e is d o m i n a n t and this “ e q u i li b r iu m c o n d i t i o n ” m a y p r e v a il f o r
several m o n th s w i t h o u t d estru ction . D u r i n g p e r io d s f r e e f r o m w a v e action
the tidal dunes, w i t h i n the s p e c ifie d area, m a in ta in a r e la t i v e ly constant
m ean w a v e le n g t h (4.5 m ± 0.3 m ) thou gh the du n es u n d erg o gra du al
change. It can be s h o w n that the ra te o f ch a n g e is such that the in d iv id u a l
dunes can m a in t a in t h e ir so n a r i d e n t it y fo r period s o f six or m o r e days.
In th e e v e n t o f a d v e r s e w e a t h e r , th e c o m b i n e d
s u p e r im p o s e d u p on tid a l f l o w
effect o f w a v e
energy
c a n d e s t r o y th e p r e v a i l i n g d u n e b e d f o r m s .
T h e m e c h a n i c s o f d e s t r u c t i o n a r e p r o b a b l y b o t t o m s h e a r s tr e s s e s e x c e e d i n g
th e
upper
th resh old
fo r
dune
sta b ility
1955)
(M a n oh a r,
and
pressure
f l u c t u a t i o n s c a u s i n g lo s s o f soil s t r e n g t h in t h e s u r f a c e s e d i m e n t s , r e s u l t i n g
in s l o p e i n s t a b i l i t y a n d
wave
co n d ition s
slu m p in g ( M i t c h e l l ,
m od erate,
the
velo cities
Tsui
becom e
&
Sangrey,
le ss
than
1972).
the
As
upper
t h r e s h o l d f o r d u n e g e n e r a t i o n , a n d d u n e s w i t h w a v e l e n g t h s r e l a t e d to th e
w a v e -in d u c e d o rb ita l d ia m e te r and th e grain
f o r m e d (In m a n , 1957; K o m a r , 1974).
size o f t h e s e d i m e n t w i l l be
W i t h fu rth e r red u ctio n o f w a v e en erg y
th e i n f l u e n c e o f t h e t i d a l v e l o c i t i e s b e c o m e s d o m i n a n t a n d t h e d u n e s i n c r e a s e
in w a v e l e n g t h u n t i l t h e t i d a l d u n e e q u i l i b r i u m
is a t t a i n e d .
T h e seven successive so n a r s u r v e y s c a rr ie d out d u r in g the post gale
p e r io d in O c t o b e r a n d N o v e m b e r 1974 s h o w the in crea se in m ean w a v e ­
len gth o v e r the p e r io d o f gale m a x i m u m + 35 h ou rs to ga le m a x im u m
-I- 203 hours.
I f it is a ssu m ed that, f o l l o w i n g r e v e rs io n to tida l c u rren t c o n tr o l, the
dune w a v e le n g t h dev elop s a c c o r d in g to the eq u a tio n :
X = X t [ 1 — exp { — ( t - t 0 )/t }1
(2 )
in w h ic h :
\ =
the m e a n w a v e len g th ca lcu la ted f r o m the seven su rv e y s f o r
po sition s near the crest o f the sa n dw aves, at m id - s lo p e and in
the tro u g h
Xj = the e q u ilib r iu m w a v e len gth (4.5 m )
t = the t im e in h ou rs f o r each o f the seven su rveys f r o m the time
o f ga le m a x im u m
f 0 = the tim e o f h y p o t h e t ic a l z e r o w a v e le n g t h
r — u t im e constant
(f„ and r w e r e ob tain ed b y p lo t tin g log X,/\] — X against t im e ) , then an
a p p r o x im a t e rate o f in crease in w a v e length o f dunes m a y be o b ta in e d
(tig. 7). T h e goodness o f lit o f the ca lcu la ted w a v e len gth s is su b jec t to
both the q u a l it y o f the sonar re co r d s and also fu r t h e r p eriod s o f m in o r
w a v e in flu ence. F o r e x a m p le , ca lcu la ted o s c illa tio n v e lo c itie s re a c h ed
23 eras - 1 at 12 m depth on 4 N o v e m b e r (ga le m a x . + 132 h o u rs ).
Time (hours)
F ig . 7. — R e v e r s i o n o f d u n e w a v e l e n g t h m e a s u r e d f r o m s id esc an s o n a r re co rd s .
U sin g the r e c o v e r y rate as o b ta in e d in e q u a tio n 2, a w a v e le n g t h / d e p t h /
tim e gra p h m a y be plotted (fig. 8) w h ic h suggests th a t 50 % o f t h e e q u il i­
briu m w a v e len gth w a s a tta in ed in a p p r o x i m a t e l y 60 h o u rs n e a r the crest
o f the sa n d w a v e, in 90 h ou rs at m id -s lo p e and in 120 hou rs in th e tro u gh ,
w h ils t 90 % r e c o v e r y w a s a tta in e d in 340, 400 and 520 h ou rs r e s p e c t iv e ly .
Fit;. 8. — R e v e r s i o n o f chine w a v e l e n g t h as a f u n c t io n o f d e p th an d t i m e .
B o th the M a r c h 1972 and M a y 1973 sequences o f data are i m p o r ta n t
f o r the u n d e rs t a n d in g o f the co n d itio n s re q u ir ed to g e n era te p a rtic u la r
du n e fo r m a t io n s . T h e f o r m e r , w h ic h consists o f one so n a r record, co n firm s
that the events o f O c t o b e r a nd N o v e m b e r 1974 are n ot unique. Calcu lated
w a v e lengths, f o r p o sition s n ea r the crest, at m id -s lo p e and in the tro u g h
(3.1 m, 2.5 m a n d 1.7 m r e s p e c t iv e ly ) at the tim e o f g a le m a x i m u m + 123
hours, w h e n c o m p a r e d w it h those o f O c to b e r and N o v e m b e r 1974 give a
g o o d c o r r e la tio n at the p o sition s n ea r the crest a n d at m id -slop e, but not
at the tro u gh p o s itio n (3.0 m, 2.7 m and 2.4 ni re s p e c t iv e ly ). T h e p o or
c o rr e la tio n in the t r o u g h position could be the result o f a change in w a te r
depth , hence a c h a n g e in w a v e - in d u c e d orbital d ia m e te r, an d / or ch ange
in g r a i n size o f the sedim ents.
T h e M a y 1973 da ta gives an in dica tion o f the w a v e co n d itio n s r e q u ir e d
to b r in g about a p a r t ia l ch a n g e in dune co n figu ra tion , as o p p o s e d to the
c o m p le te d e s tr u c tio n and r e f o r m a t i o n w h ic h p r o b a b ly o c c u rr e d in both
M a r c h 1972 and O c t o b e r and N o v e m b e r 1974.
CONCLUSION
D u r i n g p e r io d s o f intense w a v e action su p e r im p o s e d upon tidal flow,
the dunes on the fla n k o f a s a n d w a v e at L o n g s a n d H e a d are d es tr o y ed
and s u b se q u e n tly re p la c e d b y dunes w it h co n s id e ra b ly sh orter w a v e le n g th .
U n d e r tidal c o n d itio n s the dunes are re g en era ted to t h e ir tida l c o n f i g u ­
ra tio n o v e r a p e r io d o f 14 or m o r e days. I f such re d is t r ib u t io n o f sed im en ts
occurs on the fla n k s o f a sa n dw av e, then a s im ila r o r grea ter action is
to be ex p ected in the cresta l area, w h e r e both the w a v e e n e r g y and shear
stress e x e rte d b y the tidal f l o w w il l be greater. T h e field data does not
exist to m a k e it po ssib le to q u a n t i f y the changes w h i c h occu r in crestal
height, but c o n s id e r a t io n sh ou ld be giv e n to the p r e c e d i n g w a v e co nd itio n s
w h e n u n d e r t a k in g a ccu ra te b a t h y m e t r i c surveys in a sa n d w a v e area.
ACKNOWLEDGEMENTS
I wish to a c k n o w le d g e and than k the P o r t o f L o n d o n A u t h o r it y for
the use o f their Decca H i - F i x system and fo r the p r o vis io n o f w a v e data,
and also the D epa rtm en ts o f In d u s t ry and o f the E n v i r o n m e n t w h o have
p a rt ly fin anced this research. I also o w e m y thanks to m y colleagu es in
the In stitute o f O c e a n o g ra p h ic Sciences ( T a u n t o n ) w h o h a v e giv en me
advice and assistance w it h this project.
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