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ARTICLE IN PRESS
Continental Shelf Research 30 (2010) 281–292
Contents lists available at ScienceDirect
Continental Shelf Research
journal homepage: www.elsevier.com/locate/csr
Transverse structure of subtidal flow in a weakly stratified subtropical
tidal inlet
Amy F. Waterhouse , Arnoldo Valle-Levinson
Department of Civil and Coastal Engineering, University of Florida, 356 Weil Hall, Gainesville, FL, USA
a r t i c l e in fo
abstract
Article history:
Received 8 January 2009
Received in revised form
15 October 2009
Accepted 20 November 2009
Available online 3 December 2009
The transverse structure of exchange flows and lateral flows as well as their relationship to the subtidal
variability are investigated in a subtropical inlet, Ponce de Leon Inlet, Florida. Two surveys were
executed during different phases of the tidal month to determine the spatial structure of subtidal
exchange flows. Data from fixed moorings were used to depict the temporal variability of the spatial
structure established in the surveys. The data suggested a tidally rectified pattern of net outflow in the
channel and inflow over shoals with a negligible influence of streamwise baroclinic pressure gradients
on the dynamics and slight modifications due to the wind. Onshore winds strengthened net inflows but
weakened net outflows, rarely reversing them, while offshore winds increased net outflows and
weakened net inflows. Curvature effects were found to be important in modifying secondary
circulations. Slight modifications to the secondary flows were also caused by stream-normal
baroclinicity during one survey. Most important, the intensity of the exchange flows was modulated
by tides, with the largest exchange flows developing in response to the strongest tidal rectification of
spring tides.
& 2009 Elsevier Ltd. All rights reserved.
Keywords:
Subtropical inlet
Residual circulation
Subtidal flow
Tides
Florida
1. Introduction
Gregg, 1997; Lacy and Monismith, 2001)
Subtropical inlets are unique in that they are found in regions
where there is little to no net precipitation; the dynamics are
therefore free from the density-driven flow common to temperate
estuaries. Subtropical inlets have only sporadic freshwater
influence and the residual flow is typically driven by tides and
winds (Valle-Levinson et al., 2009), and modified by bathymetry
(Kjerfve, 1978; Blanton et al., 2003; Li et al., 2008; Kim and
Voulgaris, 2008). Subtropical estuaries are ideal sites for comparing observations on the spatial structure of tidal residual flow to
theoretical results as there is little to no influence from alongchannel density gradients.
Frequently, natural basins are strongly affected by channel
curvature in both bathymetry and morphology. Centrifugal
accelerations, produced by curvature, force a transverse flow
away from the channel bends at the surface and toward the
channel bends at depth (Kalkwijk and Booij, 1986). By definition,
the depth-averaged transverse flow is zero everywhere within the
inlet, and the transverse equation of motion in stratified flow
reduces to (Kalkwijk and Booij, 1986; Geyer, 1993; Seim and
@un
@un u2s u2s
g
þ us
¼
@t
@s
R
r
Corresponding author.
E-mail addresses: awaterhouse@ufl.edu (A.F. Waterhouse),
[email protected]fl.edu (A. Valle-Levinson).
0278-4343/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.csr.2009.11.008
Z Z
@r
z0
@n
dz0 þ
t
g @r
@
@un
hþ
þ b;n
Az
ro @n
@z
rh
@z
ð1Þ
where vertical advection, depth-averaged lateral advection and
Coriolis accelerations are neglected. The subscripts n and s
represent transverse and streamwise velocity components,
respectively, u is the velocity, overbars represent depth averages,
R is the radius of curvature, g is the acceleration due to gravity,
r is the water density, Z is the sea surface elevation, z is the
vertical direction, Az is the eddy viscosity, tb;n is the bottom shear
stress in the transverse direction and h is the depth of the water
column. The radius of curvature is positive when the positive
streamwise velocity (ebb, for our study) follows a clockwise
trajectory due to the curvature; thus R changes sign during
flood flow (Lacy and Monismith, 2001; Nidzieko et al., 2009). The
third term on the left-hand side of Eq. (1) is the centrifugal
acceleration term, which is generated by the streamwise velocity,
us . The first and second terms on the right-hand side of the
equation are the lateral baroclinic forcing terms. Depending on
their sign, these terms may act to oppose or enhance the
curvature-induced lateral flows (Geyer, 1993; Dronkers, 1996;
Seim and Gregg, 1997).
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Observations and modeling of flow around tidal headlands
(Geyer, 1993) and within curved estuaries have illustrated the
existence of bathymetry-induced residual eddies (Li, 2006),
enhanced vertical mixing due to channel curvature (Seim and
Gregg, 1997), the importance of lateral density gradients in
modifying the curvature-induced lateral velocities in weakly to
strongly stratified estuaries (Dronkers, 1996; Chant and Wilson,
1997; Lacy and Monismith, 2001; Huijts et al., 2009) and channels
that experience both well-mixed and stratified conditions
(Nidzieko et al., 2009). Channel curvature has been found to
affect transport of sediment and salt (Blanton et al., 2003; Kim
and Voulgaris, 2008) while tides and winds modify the magnitude
of the transverse flows (Chant, 2002).
Analytical models of residual flows within tidally driven basins
(Li and O’Donnell, 2005; Winant, 2008), when adopted in a curved
channel, show that lateral advection dominates in both long and
short curved channels with residual eddies forming on either side
of the channel bends (Li et al., 2008). In Li et al.’s (2008) model,
where a cartesian coordinate system is adopted, curvatureinduced flows and residual eddies are generated by the nonlinear
advective terms of the momentum equations. Although advection
dominates in curved channels, frictional effects of the tidal wave
entering the channel may still enhance or diminish the advective
terms and cannot be completely neglected, especially in long
channels (Li et al., 2008). The dynamics of tidally driven residual
flow can be described on the basis of a non-dimensional length.
Basins whose non-dimensional lengths are o0:620:7 are defined
as short, while those above this threshold are defined as long
(Li and O’Donnell, 1997, 2005; Winant, 2008). Basin length is the
parameter that determines the features of residual circulation
within a basin (Li and O’Donnell, 2005).
Theoretical results have been used to explain the observed
lateral structure of tidal residual flows in long basins, both straight
(Kjerfve and Proehl, 1979; Li et al., 1998; Cáceres et al., 2003) and
curved (Li et al., 2008; Hench and Luettich, 2003), as well as in
short straight basins (Winant and Gutiérrez de Velasco, 2003). Less
is known, however, about the subtidal variability or modulation of
the lateral structure of tidal residual flows in short or long basins
under the influence of curvature. Curvature-induced secondary
flow in a strongly stratified estuary increases with increasing tidal
range while the the secondary flow decreases with increasing river
discharge (Chant, 2002). Li (2006) suggests that for bathymetrically
induced residual eddies in a short, weakly stratified basin (where
curvature was not included), both wind and tidal range have little
effect on the structure or location of the residual eddies formed as a
result of these bathymetric variations.
The purpose of this study is to document, with observations,
the structure and variability of the along-channel tidal residual
flows and whether the variability of the cross-channel flows help
in the lateral redistribution of momentum in a long, subtropical,
curved inlet, Ponce de Leon Inlet, in East Central Florida. This
study also seeks to determine whether the modulation of the
residual structure is produced by either tides or winds, or both.
The subtropical nature of the inlet allows for direct observations
of the tidal residual flows as along-channel density gradients are
not influential to the dynamics.
Study
Area
8’
Atlantic Ocean
6’
5.00’
4.75’
RB
1
4.50’
B
4’
29°N
4.25’
2’
Met
Station
A
2
3
RA
4.00’
IWW
3.75’
29°N
3.50’
56.00’
55.50’
80°W
55.00’
54.50’
54.00’
58’
59’
58’ 57’ 80°W 55’ 54’
56.00’
53’
Fig. 1. Study area of Ponce de Leon Inlet, Florida which connects the Intracoastal Waterway (IWW) to the Atlantic Ocean. The moored ADCP sites are denoted with
diamonds (Stations 1, 2 and 3) and the towed ADCP survey line is denoted by a solid line across the inlet (Transect A). The CTD locations are denoted with filled circles
(Stations A and B). The thalweg of the inlet follows from CTD Station A, ADCP Station 2 and CTD Station B. The two regions of curvature are North of CTD Station B
ðRB ¼ 500 mÞ and South of CTD Station A ðRA ¼ 420 mÞ. The meteorological station (New Smyrna Beach, Station 722 361) is denoted by the black square, 4 km to the SouthWest of Ponce de Leon Inlet.
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2. Study area
Located on the Central East coast of Florida at 293 4:50 N, Ponce
de Leon Inlet is a shallow subtropical inlet (Fig. 1). Flow within the
inlet is forced by the semi-diurnal (M2) tide with a mean tidal
range of 0.6 m and typical tidal currents exceeding 1 m s1 . The
inlet has been described as having a strong ebb channel adjacent
to the North jetty (Militello and Hughes, 2000), which has been
found to be responsible for considerable scour along the northern
side of the inlet (Militello and Zarillo, 2000). Fresh water inputs
from precipitation vary seasonally, with the strongest influences
during May through September (Schwartz and Bosart, 1979).
The entrance to the inlet is 350 m wide and 12 m deep in a
channel that is o 100 m wide. The thalweg of the channel
decreases to 3.5 m within 750 m inside of the inlet. This narrow
channel is flanked, asymmetrically, by shoals that are typically
2–4 m deep. Ponce de Leon Inlet has two regions where the
channel curvature is large (in both bathymetry and morphology)
with the first curved spit occurring on the northern shore, inside
the inlet (see Fig. 1), with a radius of curvature RB of 500 m. The
second curved spit is seaward of the first, on the southern shore of
the inlet (see Fig. 1, RA ¼ 420 m). This spit is accreting northward
on both ebb and flood tides due to the curvature effect on sand
transport (Militello and Zarillo, 2000). For ebbing flows, the
curvature at RA is clockwise and RB is counter-clockwise. A twolayer curvature-induced transverse flow and possible formation of
residual eddies, downstream and upstream of the region of
curvature, are expected (Li et al., 2008).
Ponce de Leon Inlet is one of several coastal inlets connecting
Florida’s Intracoastal Waterway (IWW) to the Atlantic Ocean
(Fig. 1). The IWW, a long and narrow coastal lagoon, extends along
the entire eastern coast of Florida with a mean width of 55 m, a
mean depth of 3.5 m and a maximum depth of 5 m (Smith, 1983;
Kenworthy and Fonseca, 1996). Within the IWW significant tidal
attenuation occurs, 50 times greater attenuation than at the inlet
(Militello and Zarillo, 2000). Due to the extent of the IWW along
the East coast of Florida, the length of the Ponce de Leon InletIWW system, as defined by Li and O’Donnell (2005) and Winant
(2008), is difficult to determine and hence, will be determined
based on the observations of the tidal wave type at the entrance
to the inlet (Li and O’Donnell, 2005).
Given the shallow mean depth (4 m), Ponce de Leon Inlet can
be classified as a strongly frictional inlet with a frictional constant
(Winant, 2008) of
d¼
rffiffiffiffiffiffiffiffiffiffi
2Az
¼ 0:94
oH 2
ð2Þ
where Az is a constant vertical eddy viscosity, estimated to be
0:001 m2 s1 for this case, o is the frequency of the semidiurnal
283
(M2) tide and H is the mean depth. This frictional constant can be
calculated for an inlet to determine the frictional influence on
flow dynamics whether strong ðd ¼ 1Þ, moderate ðd ¼ 0:5Þ or weak
ðd ¼ 0:1Þ. Therefore, Ponce de Leon Inlet is a highly frictional inlet
with tidally induced residual flows that may be described for
flows at the upper end of the frictional limit as considered by
Winant (2008).
3. Data collection
In order to characterize the lateral structure of tidal residual
flows as well as the temporal variability of this structure, several
types of observations were obtained. Measurements of underway
current velocity profiles and water density profiles were combined with time series of current profiles at the entrance to Ponce
de Leon Inlet.
3.1. Underway surveys
Underway surveys were carried out at the entrance to Ponce
de Leon Inlet on September 5, 2007 and on February 21, 2008
(Transect A, Fig. 1). Both surveys stretched for nearly a semidiurnal cycle (11.2 h) during a neap tide in September and during
a spring tide in February (Fig. 2). During both surveys, a boatmounted 1200 kHz Acoustic Doppler Current Profiler (ADCP) with
bottom-tracking capability was used to measure current profiles
along cross-channel transects. The transects were sampled 15
and 17 times during the September and February surveys,
respectively. Full across-inlet coverage was ensured by sampling
within 3 m of the inlet perimeter or until the depth limited
navigation. Given the accretion on the southern spit, depths on
the southern side of the transect were very shallow. The temporal
coverage during each survey allowed for the separation of tidal
from non-tidal signals through a least-squares fit to the semidiurnal (M2) harmonic (Lwiza et al., 1991) after rotating the
currents to the principal axis of maximum variance considering
ebb and flood tides separately.
During the surveys, water density profiles were measured with
a SeaBird SBE19-Plus conductivity–temperature–depth (CTD)
profiler at the deepest part of the survey transects during every
other transect repetition (CTD Stations A and B, Fig. 1). This
allowed for the estimation of mean horizontal density gradients
and their influence on the mean flows, which was found to be
small. A surface conductivity and temperature (CT) sensor,
SeaBird SBE37, was mounted on the survey boat to capture the
lateral surface variability in the density over the tidal cycle,
recording at 0.2 Hz. Lateral density gradients proved to be larger
and more important than the longitudinal density gradients.
0.8
0.6
0.4
0.2
0
−0.2
−0.4
Aug
Sep
Oct
Nov
Dec
2008
Feb
Mar
Fig. 2. Tidal amplitude (dashed line) and subtidal water level (solid line). Periods of the towed ADCP transects are ðÞ September 5, 2007 and ð&Þ February 21, 2008. Water
level data was obtained from NOAA Tide Station 8721147 ð293 3:80 N; 803 54:90 WÞ and filtered using a low pass Lanczos-cosine filter with half-power of 60 h.
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3.2. Moored survey
Time series of current velocity profiles were obtained with
bottom-mounted ADCPs, equipped with pressure sensors, deployed at three locations across the width of the inlet. Two
instruments (Stations 1 and 3 in Fig. 1) were moored over the
shoals flanking the channel, and the third instrument was
installed in the channel (Station 2 in Fig. 1). These instruments
recorded data for 78 days distributed in two periods, from January
14, 2008 to February 25, 2008 and from February 25, 2008 to April
2, 2008. The two data sets were joined using a spline fit between
the currents and water level. During the second period the
instrument at Station 3 was damaged and the record was
unavailable. Instruments recorded the average of 400 pings
distributed over 10 min intervals at 0.5 m bins. The currents were
rotated to the principal axis of maximum variance (Emery and
Thomson, 2004) for both ebb and flood tides. Positive alongchannel currents indicated flow out of the inlet. Angles of rotation
for Stations 1, 2 and 3 were 17.5 and 20.0, 39.2 and 38.1, 41.9 and
39:13 T for ebb and flood tides, respectively. Positive cross-channel
currents were directed 903 counter-clockwise from the principal
axis.
For the purposes of investigating the secondary flows associated with curvature effects in both the moored and towed
surveys, the lateral residual flow was calculated as the anomaly
of the vertical profiles relative to the depth averaged value
(e.g. Geyer, 1993). The deployment-long average was calculated
for each mooring to characterize the lateral structure of the mean
flow. The subtidal variations were determined using a low-pass
Lanczos-cosine filter with half-power of 34 h to eliminate tidal
and inertial variations.
3.3. Atmospheric data
Local wind observations were obtained from New Smyrna
Beach meteorological station (Station 722 361 from the National
Climatic Data Centre) located at 293 30 N, 803 570 W, 4 km to the
South-West of Ponce de Leon Inlet (Fig. 1). The data were
collected at a height of 3 m and then corrected to 10 m using
the log-law velocity profile. The wind velocities, filtered with a
34-h Lanczos filter, were then rotated to be aligned with the coast
(40 and 503 T in the positive along and cross-shelf directions,
respectively) giving along and cross-shore winds and stresses,
calculated as in Large and Pond (1981).
4. Tidal and subtidal flow
4.1. Tidal information
Tidal constituents from the streamwise velocity ðus Þ and
surface elevation ðZÞ were obtained from the moored ADCPs
using T_TIDE (Pawlowicz et al., 2002; Table 1). The quarterdiurnal amplitude was greater than the diurnal amplitude from
the velocity records at both shallow moorings (1 and 3),
consistent with nonlinearities due to the depth effect on bottom
friction (Parker, 1991). The coherence squared from a crossspectral analysis between sea level and streamwise currents gave
an average phase of 1493 at the semi-diurnal tidal frequency
(1.9 cpd) indicating that tidal currents lead the water level by
1.04 h (Fig. 3b). This phase lead, confirmed by the phase difference
from the harmonic analysis (DF, Table 1), indicated that the tide
in Ponce de Leon Inlet was closer to a progressive than a standing
wave. Due to the progressive-like nature of the wave at the mouth
Table 1
Tidal amplitude (A) and phase ðFÞ and phase difference ðDFÞ of the largest of the
diurnal (K1), semi-diurnal (M2) and quarter-diurnal (M4) frequencies for the three
moored ADCPs across Ponce de Leon Inlet as calculated from streamwise velocity
ðus Þ and surface elevation ðZÞ using T_TIDE (Pawlowicz et al., 2002). The average
phase lag between surface elevation and streamwise velocity is 1493 .
M2
Constituent
A (m)
M4
F (deg)
A (m)
F (deg)
DFZ-us (deg)
Z
us
Mooring 1
K1
M2
M4
0.08
0.59
0.11
353
161
169
0.08
0.50
0.01
211
12
66
142
149
Mooring 2
K1
M2
M4
0.10
0.78
0.05
350
163
173
0.09
0.51
0.01
212
12
33
138
151
Mooring 3
K1
M2
M4
0.08
0.52
0.10
352
161
177
0.09
0.50
0.01
220
14
120
132
147
57
of the inlet, the lagoon-inlet system was likely behaving as a long
channel as defined by Li and O’Donnell (2005).
From the large d calculated in Eq. (2) and the large quarterdiurnal constituent (M4), it follows that frictional effects were
likely important. Since this inlet-lagoon system has small along
channel baroclinic pressure gradients, and the tide is the
dominant forcing mechanism, the dynamics are likely represented by the models of Li and O’Donnell (2005), Li et al. (2008)
and Winant (2008), for tidally driven flow through a highly
frictional channel of variable depth. Whether this inlet showed
similar mean flows as predicted by the theory was explored using
both moored and survey data. Given the strongly curving nature
of the inlet, a streamwise and stream-normal coordinate system
was adopted (unlike the analytical models above) in order to fully
isolate the curvature induced secondary flows and to determine
whether these lateral flows redistribute streamwise momentum
in the transverse direction.
4.2. Long term mean flows
The average streamwise flow over the entire 78 day record at
each of the mooring stations indicated vertically averaged outflow
in the channel (Station 2) and inflow over the shoals at Stations 1
and 3 (Fig. 4). Lateral velocity showed vertical shears with bottom
flow toward the northeast (NE) and surface flow toward the eastnortheast (ENE) at Station 2. The vertical structure of the lateral
velocities was consistent with curvature-induced secondary flow
of Kalkwijk and Booij (1986) around a negative bend on ebb.
A similar helical structure was observed at Station 1, with less
shear in the lateral flows.
The differences between mean ebb and flood flows illustrated
the tidal evolution of the streamwise and lateral flows. At Station
2, typical curvature-induced lateral flows occurred during ebb,
with surface flows pushed southward (away) from the inshore
bend ðRB Þ and bottom flows directed back toward the bend.
However, during flood, the flow was likely still under the
influence of RA as the lateral flows showed surface flows directed
northward at the surface, and return flows toward the spit, RA , at
the bottom. These lateral patterns were observed throughout
nearly the entire moored observation period and will be discussed
further in the next section. To investigate the consistency of both
the streamwise and lateral structure of the flow, the survey across
the mouth offered a more detailed spatial resolution of the mean
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285
|Coherence|2
1
0.5
Phase angle (degrees)
0
0
1
2
3
4
5
6
0
1
2
3
Frequency (cpd)
4
5
6
−120
−150
−180
Fig. 3. (a) Coherence squared and (b) phase of the streamwise velocity and water surface elevation from Station 1 (thick line, o’s) and from Station 2 (thin line, x’s) from the
bottom bins of each ADCP. Confidence interval (95%) is 0.26 for both current meters and is represented by dashed line in (a). Phase at 1.9 cpd indicates a 1473 phase lag
between streamwise currents and sea surface elevation.
Bottom
5.00’
Surface
4.75’
1
2
29°N
4.50’
3
4.25’
2 cm/s
4.00’
56.00’
5.00’
55.75’
55.50’
Mean Ebb
80°W
55.25’
5.00’
4.75’
4.75’
29°N
4.50’
29°N
4.50’
4.25’
20 cm/s
4.00’
4.25’
55.00’
54.75’
54.50’
Mean Flood
20 cm/s
4.00’
56.00’ 55.75’ 55.50’ 80°W 55.00’ 54.75’ 54.50’
55.25’
56.00’ 55.75’ 55.50’ 80°W 55.00’ 54.75’ 54.50’
55.25’
Fig. 4. Deployment-long mean flow vectors at the three ADCP mooring sites in Ponce de Leon Inlet, Florida. Stations 1 and 2 show transverse shear with depth where the
thick solid arrows represent the surface flow and the thick dashed arrows represent the bottom flow indicating the importance of channel curvature. For Station 3 (with only
one bin depth), the mean flow is represented by a single vector. Mean flows during maximum flood and ebb are shown in the two lower panels and illustrate the difference
in lateral velocities between the two phases of the tide. A stronger lateral shear is observed during ebb showing the classical helical structure of curvature-induced flows.
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flow structure (where the radius of curvature is positive for ebb
flows).
4.3. Tidal and residual flows
Transects across the mouth of the inlet were measured during
one semi-diurnal tidal cycle at different phases within the
fortnightly tidal cycle and under distinct wind forcing conditions
(Fig. 2). These conditions influenced the residual flows across the
mouth of the inlet during the two sampling periods in September
and February.
4.3.1. Tidal flows
The transects at the mouth of the inlet were separated into
maximum ebb and flood (Figs. 5 and 6) to determine how the
lateral structure of the flow differed, depending on the phase of
the tide. The average at maximum ebb and flood phases showed a
distinct lateral structure, similar between the two surveys. In both
surveys, maximum flood currents occurred mid-way through the
channel during flood while during ebb, streamwise velocities
were strongest along the northern edge of the inlet, as observed
by Militello and Zarillo (2000), down to a depth of 6 m. Although
both surveys occurred during different stages of the tidal cycle,
tidal currents averaged over the channel width (from 0 to 110 m)
were similar between the two surveys (Figs. 7f and 8f).
Lateral flows differed between the phases of the tide. For both
surveys, lateral currents during maximum ebb showed flow away
from the bend (northward) at the surface and flow toward the
bend (southward) close to the bottom in the channel (Figs. 5b and
6b). During maximum flood currents, both surveys showed two
counter rotating cells of weak lateral flow across the inlet.
Curvature effects likely had less effect on the flow during flood
as the across channel transects were carried out at the entrance to
the inlet where flooding currents had not yet encountered strong
bathymetric curvature. The effect of channel curvature, indicated
by the vertically sheared lateral flows visible during ebb currents,
were investigated by calculating the centrifugal acceleration term
from the streamwise velocities, averaged over the channel width
(from 0 to 110 m).
Centrifugal acceleration ðu2s u2s =RÞ over the tidal cycle was on
the order of 104 m s2 for both surveys with positive (surface)
and negative (near bottom) components occurring at maximum
ebb and flood (1300/1900 h, Fig. 7 a and 1800/1300 h, Fig. 8 a) as
observed in other studies (Lacy and Monismith, 2001; Kim and
Voulgaris, 2008; Nidzieko et al., 2009). Although the September
survey occurred during a neap tide, centrifugal accelerations were
stronger and more well organized during this survey than during
the February spring tide survey. This was attributed to lateral
baroclinicity.
Lateral baroclinic pressure gradient accelerations were
calculated as in the second term on the right-hand side of
Maximum flood
40
0
2
65
Depth (m)
4
20 cm/s
6
90
8
115
10
12
140
0
50
100
150
200
250
300
350
400
Maximum ebb
0
40
2
65
Depth (m)
4
20 cm/s
6
90
8
115
10
12
140
0
50
100
150
200
Distance (m)
250
300
350
400
Fig. 5. Streamwise and lateral currents ðcm s-1 Þ during (a) maximum flood and (b) maximum ebb across Transect A from Ponce de Leon Inlet on September 5, 2007.
Asymmetry over the tidal cycle is noted by the change in position of the velocity maxima between flood and ebb tides. North is on the left-hand side of the figure, and
positive velocity is toward the north (in the lateral direction).
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287
Maximum flood
0
40
Depth (m)
2
65
4
20 cm/s
6
90
8
115
10
12
0
50
100
150
200
250
300
350
400
140
Maximum ebb
40
0
Depth (m)
2
65
4
20 cm/s
6
90
8
115
10
12
0
50
100
150
200
250
Distance (m)
300
350
400
140
Fig. 6. Streamwise and lateral currents ðcm s1 Þ during (a) maximum flood and (b) maximum ebb across transect A from Ponce de Leon Inlet on February 21, 2008.
Asymmetry over the tidal cycle is noted by the change in position of the velocity maxima between flood and ebb tides. North is on the left-hand side of the figure, and
positive velocity is toward the north (in the lateral direction).
Eq. (1), g=rDr=Bh, where B is the width of the inlet. Given the
outflow along the northern side of the inlet during ebb tide as
observed by Militello and Zarillo (2000) and in Figs. 5 and 6, the
location of the density minimum was likely a result of differential
streamwise advection (Dronkers, 1996; Lacy and Monismith,
2001). Differential advection caused the minimum in density to
be located along the northern edge of the inlet. The actual density
minimum varied in position between towed surveys from the
northern side of the inlet (80 and 60 m from the northern edge of
Transect A for September and February surveys, respectively). In
both surveys, a marked minimum in density occurred at the end of
ebb (Figs. 7b and 8b) and the surface baroclinic pressure gradient
was stronger during September than in February (Figs. 7c and 8c).
Further inside the inlet, the baroclinic effect on the lateral
flows was observed from the mooring data at Station 2 (Fig. 9)
which was under the effect of RB on ebb and RA on flood. The
vertical shear in the lateral velocities, Dun , was calculated as the
difference in lateral velocity between the top and bottom bins of
the ADCP. Low density water, at the moorings, exits the inlet
following the northern edge of the shore. As ebb progresses,
lateral baroclinic pressure gradients develop, acting in the same
direction as the centrifugally forced flow (at the surface at RB )
causing an increase in the vertical shear in the lateral currents
ðDun Þ from mid-ebb until the beginning of flood.
Although streamwise friction was likely a strong influence on
the streamwise dynamics within the inlet, lateral bottom friction
was an order of magnitude smaller than streamwise bottom
friction as calculated using CD un jVj=H, where jVj is the magnitude
of the velocity and CD is the drag coefficient (CD ¼ 0:0025; Figs. 7f
and 8f). Modifications to the flow over the tidal cycle by the
processes mentioned above were linked to the observed residual
flows in both the streamwise and lateral velocities as explained
next.
4.3.2. Streamwise residual flows
Streamwise residual velocities had a similar structure during
both surveys (Figs. 10 and 11). Streamwise and lateral residual
velocities were calculated by removing the tidal signal from the
observed data through a least-squares fit to the semi-diurnal (M2)
tide (Lwiza et al., 1991). During September, weak inflow of
5 cm s1 was present in the first 50 m of the transect with
maximum inflow velocities confined to 3 m depth. Southward of
50 m along the transect, the streamwise residual flow was
directed into the inlet where maximum inflow currents
occurred over the shoals up to 20 cm s1 . During February, the
streamwise residual flow showed outflow on the northern side of
the inlet (0–75 m across the inlet) with maximum currents of
20 cm s1 constrained between 2 and 6 m depth (Fig. 11). The shift
toward inflow, although relatively weak at 5 cm s1 , occurred on
the slope between 75 and 150 m. Weak, o 6 cm s1 , outflow was
observed south of the slope.
The differences in the streamwise flow between the two
surveys were due to external forcing mechanisms such as changes
in stratification, the fortnightly tidal cycle and wind effects.
Hydrographic data obtained from both surveys showed that the
water column was mixed during flood and weakly stratified
during ebb. Profiles from the end of ebb and flood are shown in
Figs. 7d and 8d. At the end of ebb, the vertical density gradient
ð@r=@zÞ at the mouth of the inlet was 1.0 and 0:2 kg m4
(for September and February surveys, respectively) while further
inside the inlet at Station 3, the vertical density gradient ð@r=@zÞ
at the end of ebb tide decreased to 0.7 and 0:01 kg m4
(for September and February transects, respectively). The tidally
averaged accelerations produced by the baroclinic pressure
gradient, /ðgH=rÞ@r=@sS (where angle brackets denote the tidal
average), were small ðOð106 Þ m s2 Þ. Over the tidal cycle,
baroclinic pressure gradients never exceeded Oð105 Þ m s2 for
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0
−4
10
0
2
0
−4
−4
5
0
−2
0
10
−2
−2
−2
−2
0
8
2
2
2
4
2
6
−2
Depth (m)
0
2
4
4
2
2
2
x 10 4
15
−4 −2 0
0
12
23
22
2
4
5
21
30 m along A
80 m along A
300 m along A
20
10
15
20
22
24
5
0
−5
| |
| |
−10
1.5
1
Ebb
0.5
0
Flood
−0.5
−1
−1.5
07/09/05 12:00
15:00
18:00
21:00
ðu2s u2s =RÞ
Fig. 7. Centrifugal acceleration
(a) variability over the tidal cycle and (b) average over the tidal cycle; (c) surface st (20 m, 60 m and 360 m from northern edge of
transect A, respectively); (d) profiles of density at end of ebb (dotted) and flood (solid) at A (thick) and B (thin); (e) lateral baroclinic pressure gradient calculated at the
surface across transect A from 60 m to 360 m and streamwise (dashed-dot) and stream-normal (dotted) bottom friction parameterizations; and (f) streamwise tidal
velocity, averaged over the channel width (0 to 110 m), across transect A from Ponce de Leon Inlet on September 5, 2007.
both surveys. Therefore, the along-channel baroclinic pressure
gradient was neglected as a mechanism affecting the tidal and
residual flow dynamics within the inlet.
In density-driven estuaries, the fortnightly spring–neap cycle
results in stronger residual flows during neap tides due to
reduced vertical mixing (Haas, 1977). Conversely in tidally driven
subtropical estuaries, the fortnightly spring–neap cycle results
in stronger residual flows during spring tides rather than
during neap tides (Valle-Levinson et al., 2009). Li et al. (2008)
suggested that the location and strength of residual eddies
in curved tidally driven inlets vary little with tidal amplitude.
The September survey occurred during a neap tide with
an increasing mean water level while the February survey
occurred during a spring tide with a decreasing water level over
the sampling period (Fig. 2). Although streamwise velocities
averaged across the channel were similar (Figs. 7f and 8f), the
residual flow in September showed unequal exchange with
significantly weaker outflow than inflow which corresponded to
a net volume flow into the inlet in agreement with increasing
water level. Similarly, given the decreasing water level during
the February survey, the residual exchange flow showed
strong outflow and weak inflow resulting in net volume flow
out of the inlet.
4.3.3. Lateral residual flows
In both surveys, transverse residual flows showed depth
variable lateral flow with a two-layer structure (average of every
other vertical profile plotted in Figs. 10 and 11). In both cases,
lateral flow at the surface was directed toward the North (away
from the bend RA ) while lateral flow below 4 m and below the
surface layer along the southern shoal was directed southward,
toward the bend ðRA Þ.
Tidally averaged lateral baroclinic pressure gradients were
stronger during the September survey while lateral residual
velocities were stronger during February. This was likely a result
of there being no lateral density gradient to counteract the
centrifugally generated flow. Weak lateral residual flows during
September were due to strong baroclinic pressure gradients
suppressing centrifugal accelerations (Seim and Gregg, 1997;
Chant, 2002; Lacy and Monismith, 2001; Nidzieko et al., 2009).
Therefore, @r=@y was likely playing a role in modifying the
residual flow within the inlet, even though the along-channel
baroclinic pressure gradient was small. Fresh water input to
Ponce de Leon Inlet is sporadic and flow forced only by centrifugal
accelerations will also likely be sporadic, depending on the
external freshwater sources. Given the strong lateral shear, the
presence of strong lateral velocities due to a weak baroclinic
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0
−2
0
0
5
0
−2
0
−2
10
0
0
−2
0
Depth (m)
0
0
0
0
8
0
2
6
0
2
2
2
4 4
289
10
x 10 4
15
−4 −2 0
0
12
27
20 m along A
60 m along A
360 m along A
26
2
4
5
25
10
24
15
24
25
26
5
0
−5
−10
1.5
1
0.5
Ebb
0
−0.5
Flood
−1
−1.5
12:00
14:00
16:00
18:00
20:00
22:00
08/02/22
Fig. 8. Centrifugal acceleration ðu2s u2s =RÞ (a) variability over the tidal cycle and (b) average over the tidal cycle; (c) surface st (20, 60 and 360 m from northern edge of
transect A, respectively); (d) profiles of density at end of ebb (dotted) and flood (solid) at A (thick) and B (thin); (e) lateral baroclinic pressure gradient calculated at the
surface across transect A from 60 to 360 m and streamwise (dashed-dot) and stream-normal (dotted) bottom friction parameterizations; and (f) streamwise tidal velocity,
averaged over the channel width (0–110 m), across transect A from Ponce de Leon Inlet on February 21, 2008.
pressure gradient may affect the redistribution of momentum
within the inlet which will be explored using the mooring data.
Also to examine the details of the modulation of residual flows
suggested by the surveys, the time series measurements were
examined next.
5. Subtidal modulation
With the knowledge that curvature is an important driving
mechanism in this inlet, the cartesian coordinate system of Li and
O’Donnell (2005) and Winant (2008) is used to study how lateral
flows helped in the redistribution of streamwise momentum. This
was examined with the variation of the advective terms in the
streamwise direction, /v@u=@yS, where u and v are along and
cross-channel velocities, respectively. Subtidal variations of the
streamwise exchange flows inside the inlet confirmed survey
observations that the pattern of outflow in the channel and inflow
over shoals persisted throughout almost the entire observation
period at all depths for Stations 1 and 2 (Fig. 12c). The subtidal
flow at Station 3 (not shown) oscillated between inflow and
outflow although the mean flow over the entire record was
negative (inflow) and small. Due to the very close proximity of
this mooring site to Station 2, the residual currents were likely
under the influence of the flow in the channel.
During positive cross-shelf winds (offshore winds on February
14 and March 8, 2008 in Fig. 12 b), the subtidal flow responded
with an increase in magnitude of the outflow in the channel
(Station 2) and a corresponding decrease of the inflow over the
shoals (Station 1). Strong northerly along-shore wind pulses
modulated the residual flow in the opposite direction with
decreased outflow and increased inflow corresponding to an
onshore Ekman transport (January 21, 2008 in Fig. 12 b and c).
Modulation of magnitude of the residual flow throughout the
observation period indicated a response of the residual circulation
due to wind effects. Variability in the subtidal water level within
the inlet was correlated with along-channel wind stress (correlation coefficient, Rc , of 0.41), while cross-channel wind stresses
were less correlated ðRc ¼ 0:12Þ. Wind effects caused water level
set-up during onshore winds due to a net transport of water into
the entire cross-section of the inlet. Correspondingly, a water
level set-down during offshore winds was related to a net
seaward transport of water throughout the cross-section of the
inlet. Remote wind effects, not related to observed winds, would
cause similar transport into the inlet (out of the inlet) during
rising (falling) water level.
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0.2
un (m/s)
0.1
0
−0.1
−0.2
15
Δun (m/s)
10
5
0
−5
−10
−15
−20
−25
−30
06/Feb/08
07
08
09
10
11
12
Fig. 9. (a) Lateral velocities, un (m/s), from the surface (solid) and bottom (dotted; positive northward) from Station 2; (b) Vertical shear in the lateral velocities
(un surface -un bottom ) from Station 2 (m/s). Negative lateral shear means centrifugally forced flow for ebb flows around the inshore bend ðRB Þ, and positive lateral shear means
centrifugal type flow from RA with weak surface lateral flows. Shading along the zeroline indicates flood (gray) and ebb (black).
Residual Velocities: September Survey
20
0
2
10
Depth (m)
4
5 cm/s
6
0
8
−10
10
12
0
50
100
150
200
250
Distance (m)
300
350
400
−20
Fig. 10. Contours of residual streamwise flow ðcm s-1 Þ as calculated from the least squares fit to the semi-diurnal tidal constituent across Transect A from Ponce de Leon
Inlet on September 5, 2007. Lateral velocities (arrows) are the anomaly of the vertical profiles relative to the depth averaged profile and the average of every other profile is
shown. North is on the left-hand side of the figure, and positive velocity is out of the inlet (in the streamwise direction) and toward the North (in the lateral direction).
Residual Velocities: February Survey
0
20
2
10
4
5 cm/s
6
0
8
−10
10
12
0
50
100
150
200
250
Distance (m)
300
350
400
−20
Fig. 11. Contours of residual streamwise flow ðcm s-1 Þ as calculated from the least squares fit to the semi-diurnal tidal constituent across transect A from Ponce de Leon
Inlet on February 21, 2008. Lateral velocities (arrows) are the anomaly of the vertical profiles relative to the depth averaged profile and the average of every other profile is
shown. North is on the left-hand side of the figure, and positive velocity is out of the inlet (in the streamwise direction) and toward the North (in the lateral direction).
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1
did not show evidence of wind effects as the wind velocity was
not strongly correlated to the magnitude of the exchange flow
(Rc o0:17 for both cross-shore and along-shore wind stress
compared to a Rc ¼ 0:63 with tidal amplitude variations). The
observed modulation of the exchange flow was consistent with
observations from a single moored time-series in a subtropical
inlet that showed strongest exchanges during spring tides
(Valle-Levinson et al., 2009). This study provides more complete
observations of the lateral structure and the source of the
modulation of these residual exchange flows.
Observations from events where the flow within the inlet was
completely unidirectional (reversed flow at Station 2) tended to
occur more frequently during neap tides with sustained winds.
During the three neap tides, January 31, February 29, March 30,
flow reversal occurred in each case. During spring tides (January
23, February 9 and 21, March 9 and 22), wind stresses were not
large enough to overcome the tidally induced residual flow. As a
result, no reversal of the flow at Station 2 was observed during
spring tides. Therefore, during neap tides when wind stress
exceeded bottom stress, flow reversal in the channel was likely
overwhelming the tidally induced residual circulation.
A basic, vertically averaged, dynamical balance in the streamwise direction within the inlet, using the Boussinesq and
hydrostratic approximations, can be approximated as
@Z
@u
ts
tb
v
ð3Þ
þ
0 ¼ g
@x
rH
rH
@y
Tidal Amplitude / LP Water Level (m)
0.5
0
−0.5
0.5
0
along shelf
cross shelf
−0.5
0.2
0.1
0
−0.1
−0.2
0
−0.5
−1
−1.5
−2
1
0
−1
1
0.5
1
0
−0.5
−1
25
08/Feb/08
22
07/Mar
291
21
Fig. 12. (a) Tidal amplitude and low-passed water level during moored
observations, ð&Þ time of February 21, 2008 towed survey; (b) low passed along
shelf (solid; positive northward) and cross-shelf (dotted; positive eastward) wind
accelerations (m/s2); (c) subtidal streamwise currents (positive seaward) from all
depths at Stations 1 (dotted) and 2 (solid); (d) lateral shear between the subtidal
streamwise currents (bottom) between Stations 1 and 2; (e) streamwise lateral
advective term; and (f) bottom friction parameterization using CD ¼ 0:0025. Solid
vertical lines denote times of large along or cross-shore winds as discussed in
Section 5 and vertical dashed lines denote spring tides.
In addition to wind effects, the residual exchange flow at the
mouth of the inlet was affected by fortnightly tidal forcing.
The strength of the net exchange flow (Fig. 12 d), as determined
by the difference between the subtidal outflow in the channel and
inflow over the shallow station, was modulated by the fortnightly
tidal cycle. The strongest exchange flows occurred during the
largest spring tides of January 23 and March 9. Other large
exchange flows developed during the spring tides of February 9,
21 and March 22. In general, the strength of the net exchange flow
where the first term is the barotropic pressure gradient related to
sea level slope, the second is lateral advective acceleration, and
the third and fourth are the surface and bottom stress terms using
parameterizations for wind and bottom frictional stresses.
Although the sea level slope was not measured during this
experiment, it was likely an important dynamical component.
In the streamwise direction, tidal curvature-induced flows will
modify the streamwise momentum equation through lateral
advective accelerations. In fact, results from the straight part of
a curved estuary by Lacy and Monismith (2001) showed that the
lateral advective term was high in regions where strong lateral
gradients in streamwise flows coincided with strong lateral
velocities. Although the magnitude of the streamwise shear
ð@u=@yÞ was dependent on the spring neap cycle, depth averaged
lateral velocities were not but were small given the curvatureinduced flow yielding a vertical average close to zero. Depthaveraged lateral advection /v@u=@yS was stronger in the channel
than on the shoal, as expected (Li and O’Donnell, 2005; Winant,
2008; Fig. 12 e). However, lateral advection was strongest at the
beginning of the record, prior to the first spring tide. The peak in
lateral advection occurred in conjunction with strong NE winds
followed by a peak in cross-shore (westward) winds. The peak in
lateral advection occurred as a result of the wind rather than from
the spring tides. Other small pulses in the lateral advective term
(in the positive direction) corresponded with strong positive
cross-shore (or negative along shore) wind events. Therefore,
although streamwise exchange flows increased during spring
tides, fortnightly variability in lateral advective accelerations was
masked by the wind stress (second and third terms in Eq. (3)).
Advective accelerations and were not sufficient to redistribute
streamwise momentum laterally. Otherwise, the lateral shears
associated with spring tides would have decreased as a result of
the lateral redistribution of streamwise momentum.
Comparing the lateral advection accelerations to streamwise
frictional accelerations (/CD U jV j=HS; Fig. 12 f), friction was the
most dominant mechanism on the shoal while both terms were
important in the channel. This was in agreement with Li and
O’Donnell (2005) and (Winant, 2008) in driving a residual flow in
a tidally dominated channel. Despite the strongly curving nature
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of the channel, residual flows were generated mostly through the
interaction between the tidal wave and depth variations.
Frictional accelerations were strongest during spring tides.
6. Conclusions
In the highly frictional Ponce de Leon Inlet, observed residual
flows were consistent with theoretical residual flows in a tidally
dominated, curved channel. Residual flow, showing moderate recirculation, was persistent at two bends in the topography: on the
lee of the upstream bend of the inlet as well as on the
downstream bend further inside the inlet. A laterally sheared
pattern of net outflow in the channel and net inflow over the
shoals in the streamwise velocity persisted under different tidal
amplitudes and most wind forcing conditions. Long term current
measurements, moored across the inlet, provided novel observational information on the variability and modulation of the lateral
flow within these subtropical curved inlets.
Observations indicated that strength of the curvature-induced
residual circulation was affected by both winds and tides. The
strength of the streamwise exchange flow across the inlet was
modulated by tidal forcing from the spring–neap cycle. Unlike
temperate estuaries, the strongest exchange flows occurred
during spring tides confirming recent observations from a single
moored time series (Valle-Levinson et al., 2009).
Along-channel winds caused unidirectional flows throughout
the inlet. The direction of these flows was dependent on whether
coastal set-up or set-down was observed, thereby reducing or
increasing the inflow or outflow component of the tidal residual
circulation. Under specific criteria of wind speed during neap
tides, unidirectional flow was observed throughout the inlet with
a reversal in the channel. In the lateral direction, centrifugal
accelerations and lateral density gradient were influential in the
dynamics. Lateral baroclinic pressure gradients acted to reduce
lateral flows at the mouth of the inlet. Advection of streamwise
shear by the lateral velocities was found to be related to the wind
(and its effect on water level) masking the variability due to the
spring–neap cycle.
Acknowledgments
This research was funded by the University of Florida Water
Institute and NSF Grant OCE-0726697. We are grateful for the
comments of two anonymous reviewers and H.E. de Swart which
helped in the clarification of the paper. We thank the divers from
Logan Diving and Salvage for the deployment and recovery of the
moored instruments. Many people were involved in the survey
ADCP collection including V. Adams, B. Basdurak, P. Cheng,
A. Coman, A. Condon, M. Deavenport, U. Gravois, T. Hesser,
J. Lee, G. Ma, M. Neves, N. Sharpe and A. Penko.
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