Estuaries and Coasts
Vol. 30, No. 1, p. 127–136
February 2007
Depth-dependent Overtides from Internal Tide Reflection in
a Glacial Fjord
ARNOLDO VALLE-LEVINSON1,*, JOSÉ LUIS BLANCO2, and MAXIMO FRANGÓPULOS3
1
2
3
Civil and Coastal Engineering, University of Florida, 365 Weil Hall, Gainesville, Florida 32611
Code 614, Observational Science Branch, National Aeronautics and Space Administration Wallops
Flight Facility, Building N-159, Room E226, Wallops Island, Virginia 23337
Fundación Centro de Estudios del Cuaternario Fuego-Patagonia (CEQUA), Avenida Bulnes 01890,
Punta Arenas, Chile
ABSTRACT: Observations of current velocity profiles and hydrography over and near a tall sill in a Chilean glacial fjord are
used to illustrate the interactions between barotropic and baroclinic tides. The character of the barotropic tide in the glacial
fjord is mixed with semidiurnal dominance. The ratio of sill height to water column depth at the study site is ca. 0.95. Water
column stratification appeared only in the upper 5 m of the water column. Current velocity variations in the stratified surface
layer were quite different to those underneath. Below the pycnocline, nonlinear interactions between semidiurnal M2 and
diurnal K1 oscillations yielded a third-diurnal distortion MK3. Most interesting, surface layer currents were distorted by the
superposition of semidiurnal M2 and sixthdiurnal M6 oscillations. The oscillations with M6 variability were identified, through
wave superposition approaches, as reflected internal tides linked to M2 tidal variations. This was confirmed by theoretical
results of stratified barotropic tidal flows interacting with abrupt bathymetry. Under the predominantly tidally mixed regime
of the study area, the distortion to surface currents caused by the reflected wave was nearly symmetric during the large tidal
ranges of the diurnal cycle. Nearly symmetric distortions resulted as the phase lag between incident and reflected waveinduced currents was small (reflected currents developing a few minutes after maximum tidal flows). During the small ranges
of the diurnal cycle, distortions were asymmetrical because of the relatively larger phase lags of the reflected signal (reflected
currents developing tens of minutes after maximum tidal flows).
wala 2003). These studies have shown that internal
tides, thus produced, generate internal motions that
propagate radially away from the ridge and that
cause strong three-dimensional flow variations as
portrayed by internal tidal rays.
In coastal environments, the conversion of
barotropic tidal flow to internal tides at abrupt
bathymetric features is ubiquitous in fjords (Stacey
et al. 1995; Stacey and Gratton 2001), because of the
relatively strong tidal currents that develop over
sills. No attempts have been made to study the
effects of such conversion on the spatial variability
of the distorted tidal flow. It is the objective of this
study to investigate the vertical structure of the
distortions to tidal flows produced by a tall sill (sill
height to total depth ratio ca. 0.95). This study is
part of a larger effort whose goal is to improve the
understanding of the physical processes leading to
high primary productivity in a glacial fjord of
southern Chile, Seno Ballena. On the basis of the
findings of tidal flow over abyssal ridges it is
hypothesized that the interaction between baroclinic and barotropic tides will produce strong depthdependent overtides and compound tides in stratified systems with sharp bathymetric features. The
objective and hypothesis were addressed with
a combination of moored and shipborne observa-
Introduction
As tidal waves propagate into coastal embayments
they may be distorted by morphological features
through the action of bottom friction, advective
accelerations, and conservation of mass (Speer and
Aubrey 1985; Parker 1991). These distortions are
better appreciated in tidal current than on sea level
records and lead to harmonics with higher frequency than the forcing frequency. For instance the
semidiurnal tide is distorted into fourthdiurnal
signals, which in turn may yield sixthdiurnal signals
upon nonlinear interactions with the semidiurnal
tide (Parker 1991; Blanton et al. 2002). Most studies
in coastal environments that have described overtides and compound tides have dealt with harmonics that are practically depth independent (Friedrichs and Aubrey 1988; Dworak and Gomez-Valdes
2005). But such generation of harmonics, or
distortion to the barotropic tides, can also develop
in the open ocean as the tidal flow interacts with
abyssal ridges (Legg and Huijts 2006). The distortion in ridges is caused by a conversion of
barotropic tides to baroclinic tides (Balmforth et
al. 2002; Llewellyn Smith and Young 2002; Khati* Corresponding author; tele: 352/392-9537 ext. 1479; fax:
353/392-3394; e-mail: [email protected]
ß 2007 Estuarine Research Federation
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A. Valle-Levinson et al.
tions of current velocity and hydrography profiles in
the vicinity of Basaure Bar, a tall sill in Seno Ballena.
It was found that internal tides reflected at the sill
and interacted with incident barotropic tides to
distort the tidal currents. Such distortion caused
currents with temporal variability that is rarely
observed. The distortions were depth dependent
because of the nature of water column stratification
in the vicinity of the sill.
STUDY AREA
Seno Ballena is a Patagonian glacial fjord located
off the Strait of Magellan in southern Chile
(72u309W, 53u409S). The fjord is ca. 15 km long
and typically , 1 km wide (Fig. 1). It is characterized by a glacier at the head of the fjord and a tall
sill, Basaure Bar or the sill , 3 m water depth at
lower low water, located ca. 7 km from the glacier.
Landward of Basaure Bar, typical depths are
, 100 m, although a small isolated basin shows
depths . 100 m. Seaward of Basaure Bar, depths
increase rapidly and exceed 200 m over a large
portion of the fjord all the way to its connection
with the Strait of Magellan. The glacier calves
during the spring and its ice is abundant on the
basins landward of the sill. The presence of ice
complicates navigation of those waters but more
markedly during ebb stages, when the ice is released
seaward. During spring and summer, melting of ice
and snow from the nearby surrounding mountains
together with the calved ice from the glacier provide
a thin buoyant layer to the fjord. It is unclear what
happens to these buoyancy sources during winter.
Tides in this area are mixed with semidiurnal
predominance and typical ranges of 2 m, reaching
ranges of 3 m. The deep cross sections of the fjord
channels and the relatively small tidal range translate into tidal currents of less than 10 cm s21 in most
parts of the fjord, except over Basaure Bar, where
they increase markedly (Valle-Levinson et al. 2006).
Winds in the region are predominantly from the
west and frequently reach speeds . 15 m s21,
hindering access to the study area. The data
reported in this study were obtained under weak
wind conditions, typically , 5 m s21. Until their
collection, the waters from this system were uncharted and the data represent novel information of
their kind. The system represents an ideal natural
laboratory to study the interactions of a stratified,
oscillating flow with a tall sill.
Fig. 1. Study area and sampling locations relative to the Strait
of Magellan, South America, and Seno Ballena with the alongfjord track (dashed line), moored measurements (circled cross)
and CTD stations (filled circles). The dotted line shows a survey
that delineated the bottom profile shown in the lower panel.
bined with observations of underway current profiles across the sill. Fixed current velocities were
measured with a 307.2 kHz acoustic Doppler current profiler (ADCP) that was pointing downward at
a depth of 0.5 m, while anchored at 3 points to
reduce horizontal excursions of the instrument.
Hydrographic profiles were obtained at both ends
of a 750 m along-fjord transect that crossed Basaure
Bar. Underway current profiles and surface hydrography were obtained along the same along-fjord
transect (Fig. 1).
The fixed ADCP was anchored over a mean depth
of 63 m and at a distance of 150 m seaward of the
sill crest (Fig. 1). It was deployed for nearly 5 tidal
cycles from 14:00 (GMT) on 14 December 2004 to
22:10 (GMT) on 16 December 2004. The instrument recorded ensembles of one hundred and
twenty 1-s pings for both water and bottom track
modes. This yielded a sample interval of 4 min and
Methods
In order to explore the interactions of a stratified
flow with a tall sill (ratio of sill height to total water
depth . 0.9), measurements of current velocity and
hydrographic profiles at fixed points were com-
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:45:54
128
Cust # 4202
Overtides from Internal Tide Reflection
allowed tracking of the bottom to monitor sea level
(tide) variations. The ADCP recorded a total of
seventy 1-m bins that covered the entire water
column. Because of a blanking interval of 0.8 m and
acoustic side-lobe effects at the bottom, the first
usable bin was centered at a depth of 2.25 m and
the last usable bin was ca. 6 m above the sea bed.
The data set obtained from this deployment
recorded the phenomenon upon which this study
concentrates.
The along-fjord transect was sampled for a semidiurnal tidal cycle from 09:30 to 22:00 on 16
December 2004. A total of 27 transect repetitions
were carried out during that period. Another
307.2 kHz ADCP was mounted on a 1.4 m long
catamaran and towed at speeds of 1.5 m s21 on the
starboard side of the M/V Cabo Tamar I. The ADCP
collected 1-m bins at 2-s intervals, with the first
usable bin centered at 2 m. Current profiler data
were trimmed according to the criteria presented in
Valle-Levinson and Atkinson (1999) and interpolated to uniform grids with spacing of 20 m in the
horizontal by 1 m in the vertical. Least-squares
regression analysis was performed at each grid point
with a time series of 27 points, corresponding to
each transect repetition (e.g., Valle-Levinson and
Atkinson 1999). The frequencies fitted in the
regression were the semidiurnal M2 (period of
12.42 h), fourthdiurnal M4 (period of 6.21 h), and
sixthdiurnal M6 (period of 4.14 h) harmonics. This
procedure illustrated the spatial variability of the
semidiurnal tidal currents and the extent of their
overtides.
Simultaneously to the towed ADCP data collection a conductivity-temperature-depth (CTD) profile was recorded with a SeaBird SBE-19 at the end
of each transect repetition. A total of 13 CTD
profiles were obtained for each of the two end
points of the transect. The CTD data were processed
according to the protocol suggested and the
software provided by the instrument’s manufacturer
to convert data to ASCII format, align sensors, and
edit loops while the profile was recorded. These
profiles helped characterize the water column
stratification on either side of the sill and the
nature of its temporal variability.
Results and Discussion
The main finding of this investigation was the
depth dependence of overtide production in the
vicinity of a shallow sill in a glacial fjord. This was
attributed to the reflection of internal tides at the
sill crest. In order to arrive at the main finding and
its justification, the results are organized as follows.
The record obtained by the ADCP anchored for
2.5 d seaward of Basaure Bar is depicted first to
illustrate the nature of the flow variability through-
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:45:56
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129
Fig. 2. Time series of vertical profiles of flow recorded seaward
of the sill at the circled cross in Fig. 1. In the contour
representation for all depths, positive values, circumscribed by
the black contour line, indicate seaward flows. The lower panel
shows time series at two different depths.
out the water column. This is explained through
interaction of different tidal current harmonics at
different depths, suggesting internal tide reflection
within a surface layer delimited by the pycnocline.
The pycnocline limits and the depth-dependent
nature of the flow variability are described with
intratidal fluctuations of hydrographic variables
recorded at both ends of an along-fjord transect
that crossed the sill crest. The nature of the water
column stratification and pycnocline position is
used in a theoretical solution that explains internal
tide reflection. The spatial structure of the depthdependent nature of the flow is elucidated with the
amplitude of the semidiurnal tidal flow and its main
overtides (M4 and M6) as obtained in the alongfjord transect.
VELOCITY PROFILES AT A FIXED LOCATION
The presentation of flow fields centers exclusively
on the east component of the flow. This component
showed the maximum variance as it was aligned with
the main orientation of the fjord at the study site
(Fig. 1). The flow variability as a function of depth
and time displayed expected features, on one hand,
but peculiar features on the other (Fig. 2). Expected features were the appearance of stronger
ebb than flood flow at the surface and the opposite
at depth. Peculiar features included the limitation
of ebb flows to depths , 6 m and flood flows in the
upper 30 m of the water column. Flood flows
showed a downward phase propagation of 25 m in
0.07 d, i.e., near-surface floods occurred earlier
than flood flows at 25 m by 101 min. This was in
contrast to relatively shallow estuaries where tidal
current phases occur first near the bottom and
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A. Valle-Levinson et al.
propagate toward the surface (Valle-Levinson and
Lwiza 1995). The phase shift illustrated in Fig. 2 was
attributed to a Bernoulli suction of below-pycnocline waters caused by surface waters accelerating
during their passage over the sill (Seim and Gregg
1997; Valle-Levinson et al. 2006). The acceleration
of currents as they flow over the sill crest creates
a low pressure area that triggers aspiration of belowpycnocline waters toward the sill crest. The most
fascinating peculiarity of the record of Fig. 2 was the
depth-dependent distortion of the tidal currents.
Near the surface, just above sill crest depth, tidal
flows showed oscillations that were completely
different from those at 9.5 m depth, below sill crest.
The near-surface oscillations were distinct from any
semidiurnal oscillation depicted by predominantly
barotropic tidal flows. It is the nature of these nearsurface oscillations, and the possible reasons for
their shape, that are the focus of the remainder of
this paper.
The predominant frequency of the oscillations
sampled throughout the water column was determined with spectral amplitudes at different
depths (Fig. 3). The spectral amplitudes showed
largest values in the upper 5 m of the water column
and at the semidiurnal (M2) and sixthdiurnal (M6)
frequencies. The surface layer, dominated by the
semidiurnal harmonic and its odd overtide (Parker
1991), was limited by the base of the pycnocline as
described in the following subsection. Below the
surface layer, the dominant frequencies were
different; the semidiurnal still was influential but
also the diurnal contributed to the variability. The
M6 was not influential whereas there was some
contribution from fourthdiurnal (4 cycles per day)
and third-diurnal (3 cycles per day) harmonics. A
better idea on the contributions to the observed
signal by each harmonic was obtained from a harmonic analysis at each ADCP bin.
The amplitude of the main contributors to the
tidal currents showed strong depth-dependence
(Fig. 3). Below the sill crest depth of 3–4 m and
down to a depth of 30 m, the main harmonics were
M2, K1, and MK3. The harmonic fit was best at
depths , 27 m, where the 6 harmonics drawn
explained . 60% of the variability of the observed
flow. At a depth of 9.5 m (flow shown in Fig. 2), the
M2, K1, and MK3 explained 64% of the total
variability, whereas all 6 harmonics explained 66%
of the variability. This analysis suggests that the
oscillations at 9.5 m (Fig. 2) were caused chiefly by
the M2 and K1 and by their nonlinear interactions,
which generated the MK3 (Parker 1991; Dworak and
Gomez-Valdes 2005). Above the sill crest depth, the
dominant harmonics were the M2 and M6. The 6
harmonics drawn in Fig. 3 explained 89% of the
near-surface flow variability, but the M2 and M6
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:46:03
Fig. 3. Contours of spectral amplitude (cm s21) at different
depths from the record shown in Fig. 2, profiles of current
amplitude for different harmonics derived from a least-squares
regression to those harmonics, and goodness of fit of
the regression.
alone explained 78% of the variability. The nearsurface variations could be explained mostly with
a semidiurnal signal and a sixthdiurnal signal that
was, remarkably, nearly one half the amplitude of
the semidiurnal. It is noteworthy that the M6 is
customarily produced by nonlinear interactions
between the M2 and M4 and typically the M6 is
, 10% of the M2 amplitude, when it appears
(Parker 1991; Blanton et al. 2002). But among all 6
harmonics included in the near-surface analysis, the
M4 was the weakest contributor to the observed flow
variability. It is clear that the M6 fluctuations were
not produced by nonlinear interactions between M2
and M4. Two main questions that arise then are:
how were the M6 fluctuations generated, and why
did they only appear in depths shallower than the
sill crest?
To address the first question, it is noted that the
simple superposition of M2 and M6 waves results in
variability that is very similar to that observed
130
Cust # 4202
Overtides from Internal Tide Reflection
131
Fig. 4. Interaction between M2 (dark line) and M6 (dashed line) resulting in the shaded curve. The interaction resulting with M6
extremes occurring at the same time as M2 extremes but with opposite sign is shown in the upper left panel. The interaction with M6
extremes occurring p/6 later than M2 extremes and with opposite sign appears in the upper right panel. The lower panels are analogous to
the upper panels but for an M6 with different shape, emulating a reflected wave. In the lower right panel the reflected wave is shifted by p/
30. The vertical dash-dot line is drawn to illustrate phase shifts, which are zero in the left panels and different from zero in the right panels.
(Fig. 4). In order to produce a similar variability to
that observed, the superposition should be in such
a way that the most negative values of M6 appear at
the same time or soon after the most positive values
of M2 and vice versa. This could be thought of as
a reflected wave that interacts with an incident wave
to produce a distorted wave (shaded waves in
Fig. 4). A reflected wave that also has M6 variability
is illustrated in Fig. 4. In that case, the M6 variability
arises from the nonlinear interaction sin(sM2t) 3
|sin(sM2t)|, where sM2 is the frequency of the M2
wave and t is time. This is because |sin(sM2t)|, the
absolute value of the harmonic, has similar behavior
to that of M4 (Parker 1991). The values of M6 are
extreme, but with opposite sign, when M2 attains its
extremes or soon afterward. The interaction of M2
and M6, as portrayed by the shaded oscillation,
results from the phase shift between incident and
reflected waves. Note that the wave with M 6
frequency in Fig. 4, which can be simply regarded
as a reflected wave of the M2 wave, is most intense
around the M2 extremes and is zero (no reflection)
around the equilibrium points (zero in the ordinate). The M6 fluctuations should really be representing the reflection of semidiurnal tidal waves at
Basaure Bar. The M6 obtained from harmonic
analysis is likely the synthetic result that physically
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:46:16
131
represents the interaction between incident and
reflected waves.
The idea of tidal reflection is supported by
investigations of stratified flows past deep ocean
ridges (Balmforth et al. 2002; Llewellyn Smith and
Young 2002; Khatiwala 2003). These investigations
indicate that the interaction between barotropic
tides and steep bathymetry results in the generation
of internal tides on both sides of the abrupt
bathymetry (St. Laurent et al. 2003; Legg 2006).
Internal tide generation at abrupt bathymetry helps
explain why the observed M6 fluctuations near
Basaure Bar only appeared near the surface. But
before exploring these concepts in detail, the
hydrographic variations at either side of Basaure
Bar are described. This is done to link the base of
the pycnocline to the vertical limit of sixthdiurnal
fluctuation dominance in the supertidal band.
INTRATIDAL VARIABILITY OF HYDROGRAPHY AT EITHER
SIDE OF BASAURE BAR
Fluctuations of salinity, temperature, and density
anomaly at either side of the sill (Fig. 5) showed
different frequencies at different depths. Closest to
the surface at 1 m depth, at least two pulses of cool,
low salinity water were observed. Between depths of
5 and 10 m, there appears to have been 3 pulses on
Cust # 4202
132
A. Valle-Levinson et al.
Fig. 5. Time series of hydrographic profiles at the ends of the along-fjord transect shown in Fig. 1, denoted by filled circles. Station 1 is
seaward and station 2 is landward of Basaure Bar. Station 1 is ,250 m closer to the sill than station 2. Salinity, temperature and sigma-t
contour intervals are 0.5, 0.2uC and 0.5 kg/m3, respectively. The minor ticks on the abscissa represent 24-minute intervals. The white marks
represent times of CTD casts.
the seaward side, close to the sill (Station 1 in
Fig. 5). No distinguishable cycle was discerned
underneath depths of 4 m on the landward side,
farther from the sill (Station 2 in Fig. 5). Underneath depths of 15 m, hydrographic variations
were much weaker than those near the surface on
both sides of the sill. It was evident that the largest
vertical gradients appeared in the upper 4–5 m,
approximately at and above the sill crest. It appears
then that the sill interactions with the flow were
greatly responsible for the hydrographic variability
in the vicinity of the sill and that they could produce
internal waves. The main points to make here are
that the core of the hydrographic fluctuations was
found in the upper 5 m of the water column, and
that the fluctuations were likely related to internal
tides and overtides. The essence of investigations of
internal tide generation from barotropic tide interacting with steep bathymetry is used next to support
the argument that the observed flow and hydrographic variability in the vicinity of Basaure Bar was
produced by reflection of internal tides.
is followed here to explain the flow variability
observed near Basaure Bar. Barotropic tides that
flow over a knife-edge (zero width) ridge of height
h0 in a water column of uniform depth H are
expected to produce a baroclinic response (see St.
Laurent et al. 2003, fig. 1). The ridge has then
a nondimensional height d equal to h0/H. For the
case of Basaure Bar in Seno Ballena, d , 0.95. If the
ridge is located at x 5 0 and the barotropic flow of
amplitude U0 and frequency s is represented as
U0cos(st), then the baroclinic flows (u1, u2, w1, w2)
may be obtained through modal solutions (see St
Laurent et al. 2003 and references therein for
a detailed explanation):
npz
cosðkn x z st Þ,
H
n~1
?
npz X
u 2 ~ U0
bn cos
cosð{kn x z st Þ
H
n~1
u 1 ~ U0
INTERNAL TIDE GENERATION OVER
ABRUPT BATHYMETRY
an cos
?
X
an sin
n~1
?
X
132
Cust # 4202
(1)
npz sinðkn x z st Þ,
H
npz w2 ~ {aU0
bn sin
sinð{kn x z st Þ
H
n~1
w1 ~ aU0
The study of St. Laurent et al. (2003), which
extended those of Larsen (1969) and Robinson
(1969) on scattering of waves off a knife-edge ridge,
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:46:28
?
X
(2)
Overtides from Internal Tide Reflection
133
Fig. 6. Solution represented by equations 1 and 2 at different phases of a tidal cycle for a of 131023 and d of 0.95. The ridge is at x 5 0.
Shaded contours represent the horizontal component of the flow u (normalized by the barotropic tide U) to highlight the internal tide rays
or beams emanating from the ridge top and bouncing up at the bottom. Arrows depict both horizontal and vertical components of flow.
Depth is normalized by the total depth H (5100 m) and horizontal distance is normalized by H/a. The non-dimensional distance of 1 is
equivalent to 100 km. Note that the wave interaction may produce u/U . 1, as in St Laurent et al. (2003).
where a (appearing in w1 and w2) is the slope of the
internal wave rays, given by the ratio of horizontal to
vertical wave numbers, i.e., a 5 |k/m| 5 (s2 2 f 2)K
3 (N 2 2 s2)2K; f is the inertial frequency (Coriolis
parameter) and N is the buoyancy frequency; kn are
horizontal wave numbers; np/H are vertical wave
numbers (mn); and an and bn are the coefficients
(nondimensional) of the modal series. The subscripts 1 and 2 denote solutions on the x . 0 (e.g.,
landward of the ridge) and x , 0 (e.g., seaward of
the ridge) portions of the domain, respectively.
These solutions are based on matching conditions
at x 5 0, which allow an 5 bn. The modal coefficients
an are obtained from the matrix problem
Amn | an ~ cm
ð3Þ
and
cm ~
sinmpð1 { dÞ
:
m
But Amn is singular (the denominator is zero) when
m 5 n and cm is singular when m 5 0. Following St.
Laurent et al. (2003), the singularity coefficients
may be evaluated as:
Ann ~
npd { sin npð1 { dÞ cos npð1 { dÞ
2n
{ sin2 npð1 { dÞ
2n
c0 ~ {pd:
Amn
{ m cos npð1 { dÞ sin mpð1 { dÞ
z
(m 2 { n 2 )
n { n cos npð1 { dÞ cos mpð1 { dÞ
(m 2 { n 2 )
ð4Þ
{ m sin npð1 { dÞ sin mpð1 { dÞ
(m 2 { n 2 )
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:46:40
133
ð6Þ
and
where
n sin npð1 { dÞ cos mpð1 { dÞ
~
(m 2 { n 2 )
ð5Þ
ð7Þ
Solving the matrix problem in Eq. 3 for 200
modes, a of 1 3 1023 and d of 0.95, yields the
solutions to Eqs. 1 and 2 as depicted in Fig. 6 in
nondimensional coordinates. The ordinate has
been normalized by the total depth H and the
abscissa has been normalized by a21H. The flow
fields illustrate two main concepts. The generation
of internal tides on both sides of the ridge as
portrayed by the wave rays (beams of distinctly
shaded contours) that project from the top of the
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134
A. Valle-Levinson et al.
Fig. 7. Same as Fig. 6 but zooming in to the region 20.25 # x # 0.25.
ridge to the bottom of the domain. More important
to the study in Seno Ballena is the flow on top of the
ridge moving in opposite direction to the flow on
either side of the ridge, when the latter is near its
maximum. This is also illustrated by flow magnitudes, represented by shaded contours in Fig. 6,
spreading symmetrically away from the ridge at
different stages of the tidal cycle.
The oppositely directed flows at the ridge top and
at positions away from the ridge are best illustrated
by zooming in to the area of the ridge (Fig. 7). It is
seen that in the early stages of the tide, denoted by
the near-surface flow us at a nondimensional distance of 6 0.2, the flow over the ridge accelerates
and goes in the same direction as us. At maximum
flows, the near-surface flow over the ridge crest goes
in opposite direction to us. This is likely what was
observed in Seno Ballena as depicted in Fig. 2. The
answer to the questions posed earlier related to the
generation and vertical extent of the M6 fluctuations has to do with the generation of internal tides
that reflect at the sill crest.
The nature of the wave reflection can explain the
diurnal inequality of the tidal current distortion
observed in Fig. 2. This inequality in the distortion
has to do with the phase lag between the incident
and reflected wave-induced flows (Fig. 8). When
there is no phase lag between incident and reflected
signals, the distortion is symmetric. But as the lag
between incident and reflected flow increases, the
distortion becomes asymmetric. The lag between
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:46:53
incident and reflected wave-induced flows is ultimately related to the range of the barotropic tide.
During the largest tidal drops, the distortion was
nearly symmetric (11:30 on December 15 and 12:00
on December 16 in Fig. 9), whereas during the
small-range tidal ebbs, the distortion was asymmetric (23:00 on December 14 and 00:00 on December
16 in Fig. 9). This was related to stronger incident
and reflected flows during the large tidal drops
(light shaded areas in Fig. 9) that caused smaller
phase lags and more symmetric distortions, relative
to the small drops (dark shaded areas in Fig. 9).
The spatial extent of the interaction between
barotropic and baroclinic (internal) tides may be
determined with the underway velocity profiles
measured across Basaure Bar.
VELOCITY PROFILES ACROSS THE SILL
The semidiurnal tidal currents derived from the
27 repetitions of the along-fjord transect were most
noticeable in a surface layer , 10 m (Fig. 10). This
layer seems to have been limited to the stratified
region of the water column, i.e., delimited by the
pycnocline base. The large vertical gradients in tidal
current amplitude also suggest the influence of
internal tide generation. Otherwise barotropic tidal
currents would decrease more uniformly with depth
than the pattern observed. The semidiurnal current
amplitude showed a marked increase over the sill
crest that was asymmetrically distributed in favor of
134
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Overtides from Internal Tide Reflection
135
Fig. 9. Tidal heights and corresponding near-surface tidal
currents recorded by the current profiler. Figure illustrates
observed nearly symmetric distortions to semidiurnal currents
caused by large tidal drops (lightly shaded areas) and strongly
asymmetric distortions caused by small range tidal drops (dark
shaded areas). Nearly symmetric distortions are favored by small
phase lag between incident and reflected waves and asymmetric
distortions result from larger phase lags between incident and
reflected waves.
Fig. 8. Symmetric and asymmetric distortions (thick dark line)
arising from the interaction between an incident tide (continuous
thin line) and a reflected tide (dotted line) depending on the
phase of the reflected tide (as indicated by the vertical
dashed line).
the ebb or to the downstream side of the sill. This
suggests that there was more semidiurnal energy
dissipation on the landward basin than on the
seaward side of Basaure Bar. This could have been
caused by enhanced convective mixing that developed as dense water, brought over the sill,
encountered less dense water. Otherwise the semidiurnal tidal amplitude should have been symmetrical just like the M6 and M4 amplitudes were nearly
symmetric within the upper, stratified layer. The
distribution of the M6 amplitude shows greater
coverage than the M4 and gives an idea of the spatial
extent of the reflected internal tide near the
surface. The M4 distribution indicates a tidal distortion at this frequency that is restricted to the near
vicinity of Basaure Bar and did not reach the
mooring site. That is why it was not observed there.
Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:47:08
135
Fig. 10. Spatial distribution of semidiurnal, sixthdiurnal and
fourthdiurnal tidal current amplitudes across Basaure Bar.
Contour interval is 5 cm s21.
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The M4 distribution also had very weak vertical
structure, unlike the M6 and M2. This depthindependent distribution suggests that the M4 was
generated by nonlinear interactions of the barotropic tidal flow with the sill, most likely through
bottom friction (Parker 1991; Blanton et al. 2002).
The findings of this study are among the very few to
illustrate with field measurements (e.g., Allen and
Simpson 1998) the consequence of reflected internal tides generated at steep bathymetry in
a semienclosed coastal environment. Worthy of
mention was the production of overtides in numerical simulations of oscillating stratified flow past
abrupt bathymetries (Legg and Huijts 2006),
evidence of which was observed in Seno Ballena.
Also worthy of mention for future investigations is
the potential effect on these observations of phase
lags between the tides of the Pacific Ocean and the
tides of the Atlantic Ocean that enter the Strait of
Magellan.
ACKNOWLEDGMENTS
This study was funded by the Centro de Estudios del
Cuaternario Fuego-Patagonia (CEQUA) financed by the Chilean
Government. We thank our colleagues R. Torres, M. Hamame, O.
Mancilla, as well as the captain and crew of the M/V Cabo Tamar
for their help and dedication during data collection. A. ValleLevinson acknowledges support from National Science Foundation project 9983685. Conversations with L. Sanford, H. de Swart,
A. Kennedy, A. Sheremet, and K. Huijts were very fruitful in the
development of the ideas in this manuscript.
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Estuaries and Coasts estu-30-01-16.3d 23/2/07 14:47:21
Received, April 10, 2006
Revised, July 11, 2006
Accepted, July 16, 2006
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