# Lateral Circulation in a Partially Stratified Tidal Inlet

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{3}s

^{−1}[23]. Barataria Pass is an 800 m wide narrow channel. It is one of the four main tidal passes of Barataria Bay, accounting for ~66% of total water exchange [24]. Tidal currents account for ~85% of the total flow variance in the inlet, with equal contributions from the O

_{1}and K

_{1}constituents. Tidal amplitudes for both O

_{1}and K

_{1}constituents are about 0.5 m s

^{−1}[25]. Maximum tidal currents reach as high as 2 m s

^{−1}during tropic tides.

#### 2.2. Model Description and Configuration

^{2}s

^{−1}. The conventional quadratic bottom friction formulation is applied, with drag coefficient C

_{d}determined by matching a logarithmic bottom boundary layer velocity to that of the numerical model at the lowest sigma-layer height. However, bottom drag coefficient over the wetlands is defined as five times greater than that in the estuarine channels, mimicking the vegetation damping effect [33].

#### 2.3. Model Forcing, Initial, and Boundary Conditions

#### 2.4. Observations

#### 2.5. Analysis Methods

## 3. Results

#### 3.1. Two-Month Water Elevation Comparisons

#### 3.2. Velocity

^{−1}, than the model simulated velocity, which has a maximum magnitude of ~1.0 m s

^{−1}. The tidal phase is in agreement with the observations. Both observed and modeled cross-channel velocities (Figure 4b) are much smaller and noisier, and the tidal signal is not clear compared to the along channel velocity component. The discrepancy between the observed and modeled velocity is, in part, due to the fact that observed velocity data points were chosen along a 530 m long transect within a 90 m band (45 m on each side [22]), while modeled velocity data points are exactly along the chosen transect.

#### 3.3. Vertical Salinity Profile

#### 3.4. Temporal Variation of Stratification in the Barataria Pass

^{3}/s during this period of time. Stratification evolution at these three locations shows distinct cross-channel variation. Within 2 h of early flood tides, stratification at all three locations decreases and reaches a well-mixed condition. Then stratification starts increasing. First the station at the western shoal quickly reaches the maximum (Figure 6a), followed by the deep channel station (Figure 6b). The station at the eastern shoal has a more moderate increase rate (Figure 6c). During the remaining period of flood tide, the western shoal experiences variation between well-mixed and stratified conditions. The deep channel and the eastern shoal are always stratified, and the latter has the largest stratification except near the end of flood. During ebb tide stratification at the western shoal is the weakest and remains almost well-mixed for the whole ebb tide. Stratification at the deep channel and eastern shoal have similar evolution, decreasing in the beginning, reaching well-mixed condition 5–6 h after ebbing, and increasing again 3 h before the slack water.

#### 3.5. Residual Currents in the Barataria Pass over One Tidal Cycle

#### 3.6. Time Series of Cross-Sectional Salinity and Currents Structures

^{2}/s, probably due to the small flood current magnitude and its shears.

^{2}/s, Figure 9h) occurs at the mid-depth and bottom boundary layer, where either tidal currents or bottom friction are strong (Figure 9e). Strong turbulence mixing tends to destratify the water column, which explains the relatively uniform salinity distribution in the deep channel and east shoal (Figure 9g).

^{2}/s) at the bottom boundary (Figure 9l). The lateral circulation pattern is similar to that at T2, but with intensified strength. The convergent zone rises to the ocean surface and the right circulation cell is now a complete circle (Figure 9j).

^{2}/s, Figure 10h). Thus, the whole water column is vertically well-mixed (Figure 10g). However, a horizontal salinity gradient exists, with higher salinity located near the channel axis, fresher water on both shoals. The western shoal is fresher than the eastern shoal (Figure 10g). This is because freshwater is flushed out of the estuary through the western shoal, as shown in Figure 7b,c. The lateral circulation shows mostly eastward currents in the deep channel across the whole water column, while the eastern shoal has a convergence area (Figure 10f).

^{2}/s, which results in the water column in the east half of the channel vertically and horizontally well-mixed (Figure 10k, T8). The water column in the west half of the channel is also vertically well-mixed, but has a weak (~1) horizontal salinity decrease westward. The structure of lateral circulation and along-channel velocity remains the same, although the maximum ebb velocity has decreased from 1.0 m/s at T7 to 0.8 m/s at T8.

## 4. Discussion

#### 4.1. Depth-Averaged Momentum Balance

#### 4.2. Driving Mechanism of Lateral Circulation

#### 4.3. Flood–Ebb Asymmetry

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Decomposition of Vectors into Along- and Cross-Channel Directions

## References

- Nunes, R.A.; Simpson, J.H. Axial convergence in a well-mixed estuary. Estuar. Coast. Shelf Sci.
**1985**, 20, 637–649. [Google Scholar] [CrossRef] - Lerczak, A.J.; Geyer, W.R. Modeling the lateral circulation in straight, stratified estuaries. J. Phys. Oceanogr.
**2004**, 34, 1410–1428. [Google Scholar] [CrossRef] - Li, C. Axial convergence fronts in a barotropic tidal inlet—Sand shoal inlet, VA. Cont. Shelf Res.
**2002**, 22, 2633–2653. [Google Scholar] [CrossRef] - Li, C.; Valle-Levinson, A. A two-dimensional analytic tidal model for a narrow estuary of arbitrary lateral depth variation: The intratidal motion. J. Geophys. Res. Oceans
**1999**, 104, 23525–23543. [Google Scholar] [CrossRef][Green Version] - Valle-Levinson, A.; Li, C.; Wong, K.-C.; Lwiza Kamazima, M.M. Convergence of lateral flow along a coastal plain estuary. J. Geophys. Res. Oceans
**2000**, 105, 17045–17061. [Google Scholar] [CrossRef][Green Version] - Chant, R.J.; Wilson, R.E. Secondary circulation in a highly stratified estuary. J. Geophys. Res. Oceans
**1997**, 102, 23207–23215. [Google Scholar] [CrossRef][Green Version] - Lacy, J.R.; Monismith, S.G. Secondary currents in a curved, stratified, estuarine channel. J. Geophys. Res. Oceans
**2001**, 106, 31283–31302. [Google Scholar] [CrossRef][Green Version] - Pein, J.; Valle-Levinson, A.; Stanev, E.V. Secondary Circulation Asymmetry in a Meandering, Partially Stratified Estuary. J. Geophys. Res. Oceans
**2018**, 123, 1670–1683. [Google Scholar] [CrossRef] - Li, C.; Chen, C.; Guadagnoli, D.; Georgiou Ioannis, Y. Geometry-induced residual eddies in estuaries with curved channels: Observations and modeling studies. J. Geophys. Res. Oceans
**2008**, 113, C01005. [Google Scholar] [CrossRef] - Wargula, A.; Raubenheimer, B.; Elgar, S. Curvature- and Wind-Driven Cross-Channel Flows at an Unstratified Tidal Bend. J. Geophys. Res. Oceans
**2018**, 123, 3832–3843. [Google Scholar] [CrossRef] - Chen, S.-N.; Sanford, L.P. Lateral circulation driven by boundary mixing and the associated transport of sediments in idealized partially mixed estuaries. Cont. Shelf Res.
**2009**, 29, 101–118. [Google Scholar] [CrossRef] - Cheng, P.; Wilson, R.E.; Flood, R.D.; Chant, R.J.; Fugate, D.C. Modeling influence of stratification on lateral circulation in a stratified estuary. J. Phys. Oceanogr.
**2009**, 39, 2324–2337. [Google Scholar] [CrossRef] - Scully, E.M.; Geyer, W.R.; Lerczak, A.J. The influence of lateral advection on the residual estuarine circulation: A numerical modeling study of the Hudson River Estuary. J. Phys. Oceanogr.
**2009**, 39, 107–124. [Google Scholar] [CrossRef] - Li, M.; Liu, W.; Chant, R.; Valle-Levinson, A. Flood-ebb and spring-neap variations of lateral circulation in the James River estuary. Cont. Shelf Res.
**2017**, 148, 9–18. [Google Scholar] [CrossRef] - Geyer, W.R. Three-dimensional tidal flow around headlands. J. Geophys. Res. Oceans
**1993**, 98, 955–966. [Google Scholar] [CrossRef] - Vennell, R.; Old, C. High-resolution observations of the intensity of secondary circulation along a curved tidal channel. J. Geophys. Res. Oceans
**2007**, 112, C11008. [Google Scholar] [CrossRef] - Lacy, J.R.; Stacey, M.T.; Burau, J.R.; Monismith, S.G. Interaction of lateral baroclinic forcing and turbulence in an estuary. J. Geophys. Res. Oceans
**2003**, 108, 3089. [Google Scholar] [CrossRef] - Nidzieko, N.J.; Hench, J.L.; Monismith, S.G. Lateral circulation in well-mixed and stratified estuarine flows with curvature. J. Phys. Oceanogr.
**2009**, 39, 831–851. [Google Scholar] [CrossRef] - Brocchini, M.; Calantoni, J.; Postacchini, M.; Sheremet, A.; Staples, T.; Smith, J.; Reed, A.H.; Braithwaite, E.F.; Lorenzoni, C.; Russo, A.; et al. Comparison between the wintertime and summertime dynamics of the Misa River estuary. Mar. Geol.
**2017**, 385, 27–40. [Google Scholar] [CrossRef] - Hunt, S.; Bryan, K.R.; Mullarney, J.C. The influence of wind and waves on the existence of stable intertidal morphology in meso-tidal estuaries. Geomorphology
**2015**, 228, 158–174. [Google Scholar] [CrossRef] - Van Maren, D.S.; Hoekstra, P. Seasonal variation of hydrodynamics and sediment dynamics in a shallow subtropical estuary: The Ba Lat River, Vietnam. Estuar. Coast. Shelf Sci.
**2004**, 60, 529–540. [Google Scholar] [CrossRef] - Li, C.; Swenson, E.; Weeks, E.; White, J.R. Asymmetric tidal straining across an inlet: Lateral inversion and variability over a tidal cycle. Estuar. Coast. Shelf Sci.
**2009**, 85, 651–660. [Google Scholar] [CrossRef] - Das, A.; Justic, D.; Inoue, M.; Hoda, A.; Huang, H.; Park, D. Impacts of mississippi river diversions on salinity gradients in a deltaic Louisiana estuary: Ecological and management implications. Estuar. Coast. Shelf Sci.
**2012**, 111, 17–26. [Google Scholar] [CrossRef] - Marmer, H.A. The Currents in Barataria Bay; The Texas A.&M. Research Foundation Project 9; Texas A.&M.: College Station, TX, USA, 1948; p. 30. [Google Scholar]
- Snedden, G.A. River, Tidal, and Wind Interactions in a Deltaic Estuarine System. Ph.D. Thesis, Louisiana State University, Baton Rouge, LA, USA, 2006; p. 116. [Google Scholar]
- Chen, C.; Beardsley, R.C.; Cowles, G.; Qi, J.; Lai, Z.; Gao, G.; Stuebe, D.; Xu, Q.; Xue, P.; Ge, J.; et al. An Unstructured Grid, Finite-Volume Community Ocean Model FVCOM User Manual, 3rd ed.; Rep. 06-0602; SMAST/UMASSD: New Bedford, MA, USA, 2011. [Google Scholar]
- Chen, C.; Liu, H.; Beardsley, R.C. An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: Application to coastal ocean and estuaries. J. Atmos. Ocean. Technol.
**2003**, 20, 159. [Google Scholar] [CrossRef] - Mellor, G.L.; Yamada, T. Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys.
**1982**, 20, 851–875. [Google Scholar] [CrossRef] - Galperin, B.; Kantha, L.H.; Hassid, S.; Rosati, A. A Quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci.
**1988**, 45, 55–62. [Google Scholar] [CrossRef] - Smagorinsky, J. General circulation experiments with the primitive equations. Mon. Weather Rev.
**1963**, 91, 99–164. [Google Scholar] [CrossRef] - Li, C.; White, J.R.; Chen, C.; Lin, H.; Weeks, E.; Galvan, K.; Bargu, S. Summertime tidal flushing of Barataria Bay: Transports of water and suspended sediments. J. Geophys. Res. Oceans
**2011**, 116, C04009. [Google Scholar] [CrossRef] - Walker, N.D.; Wiseman, W.J.; Rouse, L.J.; Babin, A. Effects of River Discharge, Wind Stress, and Slope Eddies on Circulation and the Satellite-Observed Structure of the Mississippi River Plume. J. Coast. Res.
**2005**, 21, 1228–1244. [Google Scholar] [CrossRef] - Huang, H.; Justic, D.; Lane, R.R.; Day, J.W.; Cable, J.E. Hydrodynamic response of the Breton Sound estuary to pulsed Mississippi River inputs. Estuar. Coast. Shelf Sci.
**2011**, 95, 216–231. [Google Scholar] [CrossRef] - Willmott, C.J. On the validation of models. Phys. Geogr.
**1981**, 2, 184–194. [Google Scholar] [CrossRef] - Cheng, P.; Valle-Levinson, A. Influence of lateral advection on residual currents in microtidal estuaries. J. Phys. Oceanogr.
**2009**, 39, 3177–3190. [Google Scholar] [CrossRef] - Wong, K.-C. On the nature of transverse variability in a coastal plain estuary. J. Geophys. Res. Oceans
**1994**, 99, 14209–14222. [Google Scholar] [CrossRef] - Geyer, W.R.; Signell, R.P.; Kineke, G.C. Lateral trapping of sediment in partially mixed estuary. In Physics of Estuaries and Coastal Seas; AA Balkema: Brookfield, VT, USA, 1998; pp. 115–124. [Google Scholar]
- Geyer, W.R.; Trowbridge, J.H.; Bowen, M.M. The dynamics of a partially mixed estuary. J. Phys. Oceanogr.
**2000**, 30, 2035–2048. [Google Scholar] [CrossRef] - Ralston, D.K.; Geyer, W.R.; Warner, J.C. Bathymetric controls on sediment transport in the Hudson River estuary: Lateral asymmetry and frontal trapping. J. Geophys. Res.
**2012**, 117, C10013. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Geographic location of the Barataria Estuary. S1–S6 are USGS stations. (

**b**) Location of Barataria Pass. The coordinate is defined as positive x to the eastern bank, positive y to the upstream. The red line indicates the cross-section shown in (

**c**) and is used in later analysis. (

**c**) Cross-sectional view of Barataria Pass. The black lines indicate CTD measurements. C1–C7 are locations used for 2-D momentum equation analysis.

**Figure 2.**Unstructured grid configured for the Finite Volume Coastal Ocean Model (FVCOM) Barataria Pass model: (

**a**) whole computational domain; (

**b**) local domain of Barataria Estuary; (

**c**) local domain of Barataria Pass, with horizontal resolution ~50 m in the cross-channel direction and 30 m in the along-channel direction. Contours are interpolated bathymetry. White dash line indicates cross section in this study.

**Figure 3.**Water elevation comparison between USGS observations (black) and model simulation (red) from 1 July to 31 August 2008. Grayed areas represent missing data.

**Figure 4.**(

**a**) Along-channel velocity at 1.32 m below the surface for observed (red dot) and modeled (blue dot) data; (

**b**) Cross-channel velocity at 1.32 m below the surface for observed (red dot) and modeled (blue dot) data.

**Figure 5.**Vertical profiles of salinity comparison between in situ observation (red) and simulation (black). The numbers in the plot represent the sequence of CTD casts. Left panels are for flood tides (

**a**,

**c**,

**e**), while right panels for ebb tides (

**b**,

**d**,

**f**).

**Top**,

**middle**, and

**bottom**row are at the eastern (

**a**,

**b**), middle (

**c**,

**d**), and western (

**e**,

**f**) side of the channel, respectively. Water level elevation in the deep channel is shown in the bottom-left small panel, with vertical lines showing casting times.

**Figure 6.**Time series (06:00 31 July to 07:40 1 August 2008) of water level elevation (red), depth-averaged along-channel velocity (green), and bottom-top salinity difference at (

**a**) western shoal, (

**b**) deep channel, and (

**c**) eastern shoal. Shaded area represents flood tide. Arrows show different stages during a tidal cycle.

**Figure 7.**Transverse distribution of (

**a**) flood-, (

**b**) ebb-, and (

**c**) tidally-averaged along-channel velocities, looking up-estuary (unit: cm/s). Red isolines represent flood velocities, while black isolines ebb velocities.

**Figure 8.**Transverse distribution of (

**a**,

**d**) flood-, (

**b**,

**e**) ebb-, and (

**c**,

**f**) tidally averaged cross-channel velocities (unit: cm/s, positive is eastward, negative is westward) and lateral circulation.

**Figure 9.**Cross-sectional profiles of currents $\left(u,v,w\right)$, salinity and vertical viscosity during flood tide. The first column (

**a**,

**e**,

**i**,

**m**,

**q**) is along-channel velocity, the second column (

**b**,

**f**,

**j**,

**n**,

**r**) secondary circulation, the third column (

**c**,

**g**,

**k**,

**o**,

**s**) salinity, and the last column (

**d**,

**h**,

**l**,

**p**,

**t**) vertical viscosity. The velocity contour interval is 0.2 m/s, positive is up-estuary. The salinity contour interval is 0.5. Each row corresponds to a time instance indicated by an arrow in Figure 6.

**Figure 10.**Cross-sectional profiles of currents $\left(u,v,w\right)$, salinity and vertical viscosity during ebb tide. The first column (

**a**,

**e**,

**i**,

**m**,

**q**) is along-channel velocity, the second column (

**b**,

**f**,

**j**,

**n**,

**r**) secondary circulation, the third column (

**c**,

**g**,

**k**,

**o**,

**s**) salinity, and the last column (

**d**,

**h**,

**l**,

**p**,

**t**) vertical viscosity. The velocity contour interval is 0.2 m/s, positive is landward. The salinity contour interval is 0.5. Each row corresponds to a time instance indicated by an arrow in Figure 6.

**Figure 11.**Time series of vertically averaged momentum equation terms in the cross- (

**a**–

**g**) and along-channel (

**h**–

**n**) directions during the same 25.6 h tidal cycle. The left column is for the cross-channel direction. The right column is for the along-channel direction. DDT (dash black) represents the local acceleration, AVD (red) the non-linear advection, COR (pink) the Coriolis force, DPBP (green) the barotropic pressure gradient, DPBC (blue) the baroclinic pressure gradient, AV2D (purple) the difference between 2-D and 3-D nonlinear terms, FRIC (orange) the bottom friction, and HDIF (yellow) the horizontal diffusion. Shaded areas indicate flood tide. Stations (C1–C7) from top to bottom are located from the west to the east shown in Figure 1c. Note that the y-axis scales for Figure (

**i**,

**j**) are different from others.

**Figure 12.**Transverse distributions of terms (m/s

^{2}) in along-channel momentum equation at flood (T3). Terms include (

**a**) local acceleration, (

**b**) lateral advection, (

**c**) along-channel advection, (

**d**) barotropic pressure gradient, (

**e**) baroclinic pressure gradient, (

**f**) total pressure gradient, (

**g**) horizontal stress divergence, (

**h**) Coriolis force, and (

**i**) vertical stress divergence. Red isolines represent positive values, while blue isolines negative values. Dash line shows contour 0. The contour intervals are shown in parenthesis.

**Figure 13.**Transverse distributions of terms (m/s

^{2}) in cross-channel momentum equation at flood (T3). Terms include (

**a**) local acceleration, (

**b**) lateral advection, (

**c**) along-channel advection, (

**d**) barotropic pressure gradient, (

**e**) baroclinic pressure gradient, (

**f**) total pressure gradient, (

**g**) horizontal stress divergence, (

**h**) Coriolis force, and (

**i**) vertical stress divergence. Red isolines represent positive values, while blue isolines negative values. Dash line shows contour 0. The contour intervals are shown in parenthesis.

**Figure 14.**Transverse distributions of terms (m/s

^{2}) in along-channel momentum equation at ebb (T7). Terms include (

**a**) local acceleration, (

**b**) lateral advection, (

**c**) along-channel advection, (

**d**) barotropic pressure gradient, (

**e**) baroclinic pressure gradient, (

**f**) total pressure gradient, (

**g**) horizontal stress divergence, (

**h**) Coriolis force, and (

**i**) vertical stress divergence. Red isolines represent positive values, while blue isolines negative values. Dash line shows contour 0. The contour intervals are shown in parenthesis.

**Figure 15.**Transverse distributions of terms (m/s

^{2}) in cross-channel momentum equation at ebb (T7). Terms include (

**a**) local acceleration, (

**b**) lateral advection, (

**c**) along-channel advection, (

**d**) barotropic pressure gradient, (

**e**) baroclinic pressure gradient, (

**f**) total pressure gradient, (

**g**) horizontal stress divergence, (

**h**) Coriolis force, and (

**i**) vertical stress divergence. Red isolines represent positive values, while blue isolines negative values. Dash line shows contour 0. The contour intervals are shown in parenthesis.

**Figure 16.**Cross-sectional average of lateral velocity magnitude for the 25.6 h diurnal tidal period.

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## Share and Cite

**MDPI and ACS Style**

Cui, L.; Huang, H.; Li, C.; Justic, D. Lateral Circulation in a Partially Stratified Tidal Inlet. *J. Mar. Sci. Eng.* **2018**, *6*, 159.
https://doi.org/10.3390/jmse6040159

**AMA Style**

Cui L, Huang H, Li C, Justic D. Lateral Circulation in a Partially Stratified Tidal Inlet. *Journal of Marine Science and Engineering*. 2018; 6(4):159.
https://doi.org/10.3390/jmse6040159

**Chicago/Turabian Style**

Cui, Linlin, Haosheng Huang, Chunyan Li, and Dubravko Justic. 2018. "Lateral Circulation in a Partially Stratified Tidal Inlet" *Journal of Marine Science and Engineering* 6, no. 4: 159.
https://doi.org/10.3390/jmse6040159