Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina

Water Science and Engineering 2017, x(x): 1e12 H O S T E D BY

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Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina Mohammad Nabi Allahdadi*, Chunyan Li Department of Oceanography and Coastal Sciences, College of the Coast and Environment, Louisiana State University, Baton Rouge 70803, USA Received 11 September 2016; accepted 24 March 2017 Available online ▪ ▪ ▪

Abstract Numerical experiments were conducted using the finite volume community ocean model (FVCOM) to study the impact of the initial density stratification on simulated currents over the Louisiana shelf during Hurricane Katrina. Model results for two simulation scenarios, including an initially stratified shelf and an initially non-stratified shelf, were examined. Comparison of two simulations for two-dimensional (2D) currents, the time series of current speed, and variations of cross-shore currents across different sections showed that the smallest differences between simulated currents for these two scenarios occurred over highly mixed regions within 1 radius of maximum wind (RMW) under the hurricane. For areas farther from the mixed zone, differences increased, reaching the maximum values off Terrebonne Bay. These large discrepancies correspond to significant differences between calculated vertical eddy viscosities for the two scenarios. The differences were addressed based on the contradictory behavior of turbulence in a stratified fluid, as compared to a non-stratified fluid. Incorporation of this behavior in the MellorYamada turbulent closure model established a Richardson number-based stability function that was used for estimation of the vertical eddy viscosity from the turbulent energy and macroscale. The results of this study demonstrate the necessity for inclusion of shelf stratification when circulation modeling is conducted using three-dimensional (3D) baroclinic models. To achieve high-accuracy currents, the parameters associated with the turbulence closures should be calibrated with field measurements of currents at different depths. © 2017 Hohai University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Hurricane Katrina; Louisiana shelf; Hydrodynamics; Baroclinic and barotropic models; Stratification

1. Introduction Water column stratification is a prominent feature of most oceanic, shelf, and estuarine waters. Although mixing forces, including winds, waves, and tides, occasionally or continuously mix the water column, density gradients re-stratify the This work was supported by grants from Louisiana's Coastal Protection and Restoration Authority (CPRA) and the Stennis Space Center, the Lake Pontchartrain Basin Foundation, National Science Foundation (Grants No. OCE-0554674, DEB-0833225, OCE-1140268, and OCE-1140307), the Hypoxia Project of NOAA (Grant No. NA06NPS4780197), the Shanghai Universities First-Class Disciplines Project, and the Shanghai Ocean University International Center for Marine Studies. * Corresponding author. E-mail address: [email protected] (Mohammad Nabi Allahdadi). Peer review under responsibility of Hohai University.

water column partially or fully, even in the vicinity of a hurricane's track (Keen and Glenn, 1999). Hence, these water bodies are always affected by some degree of stratification. Stratification highly modulates bio-geochemical processes across the water column and affects the concentration of different chemical substances (Katsev et al., 2010). Strong summertime stratification over the Louisiana-Texas continental shelf is the main physical contributor to the seasonal hypoxia, as it prevents re-oxygenation of bottom water (Wiseman et al., 1997; Allahdadi et al., 2013; Chaichitehrani, 2012). As a result of confinement by the stratification, colored dissolved organic matter (CDOM) is exposed to the sunlight and loses its properties through the photo-bleaching process (Tehrani et al., 2013; Chaichitehrani et al., 2014). A relevant aspect of the stratification/de-stratification impact is the contribution in terms of modulating the

http://dx.doi.org/10.1016/j.wse.2017.03.012 1674-2370/© 2017 Hohai University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Allahdadi, M.N., Li, C., Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina, Water Science and Engineering (2017), http://dx.doi.org/10.1016/j.wse.2017.03.012

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circulation. Several studies have demonstrated the substantial effect of stratification on current hydrodynamics in different water bodies (Csanady, 1972; Park and Kuo, 1996; Saenko, 2006; Zhang and Steele, 2007; Allahdadi et al., 2011, 2017). Park and Kuo (1996) pointed out that, in an estuary, mixing across the water column can weaken the circulation by enhancing vertical momentum flux, while circulation may be strengthened by increasing salinity gradients along the estuary. For a large stratified lake, the interaction between wind stress and Coriolis force can produce complicated circulation structures (Csanady, 1972). Csanady (1972) used an analytical model to study the effect of wind stress on large stratified lakes and concluded that baroclinic Kelvin waves that cause substantial transport along the shore are major features of the response to spatially uniform wind. Baroclinicity significantly contributes to the formation of a cyclonic summertime circulation pattern in Lake Michigan (Schwab and Beletsky, 2003). As an example for shelf waters, a study for the Rine ROFI demonstrated that the progression of tidal waves in stratified waters could result in significantly different current patterns, as compared to cases with pre-mixed waters. Current observation data were used along with an analytical model to conclude that tidal ellipses were substantially different for stratified and mixed conditions (Visser et al., 1994). During the well-mixed periods, tidal currents were essentially rectilinear, with the major component directed along the coast, while the stratification enhanced the cross-shore component up to about 40% of the alongshore component. Over the Gorgeous Bank, a remarkable summertime stratification effect on amplification of current speed and transport, as well as a strengthening of the tidal mixing front, was reported (Naimie, 1996; Chen et al., 2003). In the open ocean or large water bodies like the Gulf of Mexico, stratification contributes to the amplification of currents through inertial oscillations. In this case, stratification controls the rate of wind momentum exchange from the surface across the water column by controlling the vertical eddy viscosity (Davies, 1985). Studies using both observational data and numerical models have demonstrated the intensification effect of summertime stratification on shelf currents in the northern Gulf of Mexico (Chen and Xie, 1997; DiMarco et al., 2000). Hurricane winds mixing the water column produce an extreme case of stratification/mixing effects on circulation. In this case, a rather complicated spatial and temporal pattern of mixing across the water column is produced (Elsberry et al., 1976; Price, 1981). Cooper and Thompson (1989) reported that skipping the stratification could have been one of the main reasons for discrepancies between measured and simulated current speeds in the northern Gulf of Mexico during Hurricane Eloise. Consideration of an initially stratified water column and the effect of turbulent mixing across the water column is essential to some 3D numerical models used for studying hurricane-induced currents (for example, Ly, 1994; Keen and Glenn, 1999; Ly and Kantha, 1993). Keen and Glenn (1999) simulated the hydrodynamics induced by Hurricane Andrew, which passed over the Louisiana shelf in 1992,

and compared the results with available measurements at several stations. They examined both stratified and nonstratified models, and concluded that for moorings that are located within 1 RMW of the hurricane center, the results obtained from both stratified and non-stratified models agreed with the measurements. For stations farther than 1 RMW from the hurricane center, and especially farther than 2 RMW, results of the non-stratified model were significantly different from the measurements. This indicates that simulated current magnitudes are affected by the rate of turbulent energy exchange and dissipation within the water column (Allahdadi et al., 2011, 2017). The same approach was applied by Keen and Glenn (1998) to calibrating the simulated surface currents during Hurricane Andrew. They found that the overestimation/underestimation of surface/bottom currents was due to the small rate of turbulent energy dissipation. Hence, by changing the empirical parameter representing the dissipation term in the turbulent closure model, current speeds were modified to agree with the measurements. However, these studies did not address the detailed variations of currents in relation to stratification and turbulent mixing. This study attempted to examine the temporal and spatial variations of simulated currents in a stratified and non-stratified water column during a hurricane and address the role of vertical mixing in causing the differences between the simulated currents for different scenarios of the initial shelf stratification. 2. Materials and methods 2.1. Model formulation The finite volume community ocean model (FVCOM), a 3D primitive equation ocean model, was used to implement the numerical tests and study the effect of stratification on hurricane-induced circulation in the northern Gulf of Mexico. The horizontal equations of motion in a 3D case (as included in FVCOM) consider the local acceleration term, nonlinear acceleration terms, Coriolis effect, pressure gradient, and vertical and horizontal internal friction terms. Eqs. (1) and (2) include all the mentioned terms for x and y directions, respectively:   vu vu vu vu 1 vP v vu þ u þ v þ w  fv ¼  þ Km þ Fu vt vx vy vz r0 vx vz vz ð1Þ   vv vv vv vv 1 vP v vv þ u þ v þ w þ fu ¼  þ Km þ Fv vt vx vy vz r0 vy vz vz ð2Þ where x, y, and z are east-west, north-south, and vertical Cartesian coordinate axes, respectively; u, v, and w are the current velocity components in the x direction, y direction, and z direction, respectively; t is time; f is the Coriolis parameter; P is the pressure; r0 is the reference water density; Km is the

Please cite this article in press as: Allahdadi, M.N., Li, C., Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina, Water Science and Engineering (2017), http://dx.doi.org/10.1016/j.wse.2017.03.012

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vertical eddy viscosity; and Fu and Fv are the horizontal momentum diffusion terms in x and y directions, respectively. The second term on the right-hand side of each equation accounts for the effect of vertical momentum flux on currents in x and y directions. This term is a function of the vertical eddy viscosity, which is controlled by stratification across the water column (Chen et al., 2006). Determining the appropriate values for this parameter has always been a challenge in 3D circulation models. FVCOM uses the Mellor-Yamada level 2.5 turbulent closure model to parametrize the vertical eddy viscosity. In this approach, Km is determined from the following equation:

3

2.2. Model setup

where 0.5q2 is the turbulent kinetic energy, l is the turbulent macroscale, and Sm is a stability function. Parameters q and l are calculated by solving a set of differential equations, incorporated in FVCOM. Parameter Sm is a function of q, l, and the Gradient Richardson number at each depth (discussed further in Section 4). FVCOM also solves the equations for temperature and salinity variations. Hence, vertical variations of density and stratification and, thereby, the stratification strength are determined for further application in the turbulent closure model. More about the FVCOM model formulation and its numerical scheme can be found in Chen et al. (2006).

The modeling area extended from Mobile, Alabama to the Sabine Bank, Texas, and comprised Louisiana shallow and deep waters (Fig. 1(a)). A computational mesh, composed of triangular elements, which was refined over the shelf, was used (Fig. 1(b)). Mesh resolution varied from 10 km along the offshore boundary to about 500 m over the inner shelf. Fig. 2 shows the track of Hurricane Katrina in the northern Gulf of Mexico. In the vertical direction, 25 sigma layers with higher resolution at the surface were considered (Fig. 3), where layers and bed profile are plotted along section 1, and the Southwest Pass is located at an along-shelf distance of 440 km. The model was forced with a Hurricane Katrina wind field (see Fig. 2 for the track in the northern Gulf of Mexico) obtained from the combination of H-Wind and wind fields from the National Centers for Environmental Prediction (NCEP). HWind is a high-resolution hurricane wind product from the National Oceanic and Atmospheric Administration (NOAA)'s Hurricane Research Division (Powell et al., 1996, 1998). This wind field is produced using available surface weather observations including ships, buoys, coastal platforms, surface aviation reports, and reconnaissance aircraft data adjusted to the surface. The final wind field is represented at a 10-m height on a 1000 km  1000 km moving box with a spatial resolution of about 6 km centered at the hurricane's central position (Dietrich et al., 2011; Wang and Oey, 2008). In this study, a hurricane wind field was blended with the NCEP/ NARR (North American Regional Reanalysis) wind at a 36-km resolution (Allahdadi et al., 2011) to include the background winds away from the hurricane center. The main objective of this study was to demonstrate the effect of stratification on the current pattern generated only by a hurricane force. In this case, the pre-stratified water column was mixed under the pure effect of the hurricane, and all changes in stratification and current pattern could be attributed to the hurricane. Therefore, tidal forces were not included. Also, the Louisiana shelf is a microtidal region where the average tidal domain is 0.4 m (Allahdadi et al., 2013). The current induced

Fig. 1. Modeling area.

Fig. 2. Track of Hurricane Katrina in northern Gulf of Mexico.

Km ¼ lqSm

ð3Þ

Please cite this article in press as: Allahdadi, M.N., Li, C., Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina, Water Science and Engineering (2017), http://dx.doi.org/10.1016/j.wse.2017.03.012

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Fig. 3. Water depth distribution and sigma layers used for model discretization in z direction.

by this small tidal force is negligible in most cases (DiMarco and Reid, 1998). To avoid instabilities caused by the reflected waves from the boundary, the explicit Orlanski radiation (ORE) was used as the boundary condition along with the appropriate number of sponge layers. Further details about the model setup and verification with field data can be found in Allahdadi (2014) and Allahdadi and Li (2017).

constant values of 25 C for water temperature and 35 psu for salinity were used at the beginning of the simulation. Vertical eddy viscosity for both scenarios was resolved using the Mellor-Yamada level 2.5 turbulent closure model, as described in Section 2.1. Two parameters, the background eddy viscosity and the constant for calculating turbulent energy dissipation (B1), were specified for both stratified and nonstratified simulation scenarios. Note that the background eddy viscosity is a part of the vertical eddy viscosity accounting for the initial stratification conditions at the beginning of simulations, and the rest of the vertical eddy viscosity is calculated based on a turbulent closure model. The background eddy viscosity was considered 104 based on Kantha and Clayson (1994). This small value of 104 for vertical eddy viscosity at the beginning of modeling was used to account for internal wave effects at the start time. The constant for calculating turbulent energy dissipation was used to calculate the rate of kinetic energy dissipation as a tuning constant. The rate of kinetic energy dissipation in the Mellor-Yamada closure model is controlled by the following relationship: 3

2.3. Simulation scenarios To study the effect of stratification on the Louisiana shelf currents during Hurricane Katrina, two simulation scenarios, stratified and non-stratified shelves, were considered. Model setup and input parameters for both scenarios were the same, with the only difference being the initial temperature and salinity variations across the water column. For the stratified scenarios, vertical variations of temperature and salinity were introduced into the model from the climatological database, prepared by NOAA (http://www.nodc.noaa.gov/access/ allproducts.html) for August, the month in which Hurricane Katrina passed over the Louisiana shelf. Fig. 4 shows the initial temperature stratification at the beginning of the simulation across the water column for the east-west section 1 shown in Fig. 2. The patterns of initial salinity stratification and thereby density stratification are similar. For the non-stratified scenarios,

Fig. 4. Initial temperature stratification over shelf for section 1 in stratified scenario.

¼

q3 B1 l

ð4Þ

where 3 is the rate of kinetic energy dissipation; and B1 is a coefficient holding a range between 12 and 25, which was considered as its intermediate value of 16.6 in this study (Keen and Glenn, 1998). 3. Simulation results Using the model described in the previous section, simulation was completed for a 15-day period. This simulation period included a week before August 29 (the day that Katrina passed over the Louisiana shelf) and a week after the landfall in the northern Gulf of Mexico. Simulated currents for stratified and non-stratified scenarios were compared at different times, and some significant differences were identified, especially in terms of the velocity values. Fig. 5 shows the shelfwide simulated surface currents for each scenario at two different times on August 29, 2005, where the blue solid line represents the hurricane's track and the red circular points on the hurricane's track show the location of the eye corresponding to the simulation at 7:00 and 10:00 UTC. At 7:00 UTC on August 29, 2005, when the hurricane's eye was located about 50 km southwest of the Bird's Foot Delta, just west of the Mississippi Southwest Pass, northeasterly winds on the left side of the hurricane produced southward-tosouthwestward currents in the near-shore and offshore regions of Terrebonne Bay. The overall current pattern for both simulation scenarios was similar. However, the pattern of simulated currents for the non-stratified scenario was spatially smoother and more uniform, exhibiting larger velocities over the inner shelf, especially off Terrebonne Bay. The cyclonic pattern of the hurricane-induced currents is more pronounced for the stratified scenario, due to the substantial decline of simulated currents over the offshore areas under the non-

Please cite this article in press as: Allahdadi, M.N., Li, C., Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina, Water Science and Engineering (2017), http://dx.doi.org/10.1016/j.wse.2017.03.012

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Fig. 5. Simulated currents over Louisiana shelf at two different times in stratified and non-stratified scenarios.

stratified scenario. Over the offshore area of Terrebonne Bay, speeds of simulated currents under the assumption of a nonstratified water column reached 1 m/s, while, for the stratified scenario, the current speed over this area was 0.2e0.3 m/ s. At 10:00 UTC, the eye was located about 20 km southwest of the Southwest Pass. The southward and southwestward currents, flowing from the west of Terrebonne Bay toward the area in the south of Barataria Bay, were still smoother and larger in magnitude for the non-stratified scenario. Currents around the hurricane center at 10:00 UTC followed patterns for both simulation scenarios similar to those at 7:00 UTC. The difference in currents resulting from stratified and non-stratified simulation scenarios was also examined by comparing time series of current speeds at three different points (P1, P2, and P3) over the Louisiana shelf (Fig. 6). Although the adopted approaches for calculating the vertical eddy viscosity and the associated parameters are the same for both simulation scenarios, the dependency of eddy viscosity on the stability of the water column (stratification strength) can result in completely different values of eddy viscosity at a particular location. In order to explore the effect of vertical eddy viscosity on currents, for each point, the values of the vertical eddy viscosity in stratified and non-stratified scenarios (as calculated by the Mellor-Yamada level 2.5 turbulent closure model) are compared (Fig. 7). Time series of current speed and vertical eddy viscosity are presented for about 40 h, including 20 h before the time the eye reached the Southwest Pass (represented as negative values) and 20 h

after that (represented as positive values). The time that the eye reached the Southwest Pass is considered the reference time (t ¼ 0). It can be seen from Fig. 6 that, for the non-stratified scenario, the current speed peak (almost corresponding to t ¼ 0) at point P1, located about 50 km west of Katrina's track (about 1.4 RMW, when the eye was located just west of the Southwest Pass), was almost twice that of the stratified scenario. The non-stratified scenario results in almost zero current speed at t < 10 h and t > 10 h, while the stratified scenario results in current speeds between 0.15 and 0.4 m/s at t < 10 h and t > 10 h. As shown in Fig. 7, time series of calculated vertical eddy viscosity at point P1 are completely different for the two simulation scenarios. For the non-stratified scenario, the parameter has a maximum of 20 m2/s, while the stratified scenario results in very small values (less than 0.01 m2/s). For point P2, located 25 km (about 0.7 RMW) from the left side of the eye, differences between current speeds of the two simulation scenarios are smaller, as compared to point P1, but are still significant. At this location, simulated peaks of current for the stratified and non-stratified scenarios are about 0.5 and 0.7 m/s, respectively (Fig. 6(b)). The corresponding time series of the vertical eddy viscosity at a depth of 10 m depict similar variations for both scenarios. The vertical eddy viscosity increases from small values to the peak (corresponding to the approximate time when the hurricane's eye is located in the west part of the Southwest Pass) and decreases after the landfall. However, for the stratified scenario, the values are

Please cite this article in press as: Allahdadi, M.N., Li, C., Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina, Water Science and Engineering (2017), http://dx.doi.org/10.1016/j.wse.2017.03.012

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Fig. 7. Comparison of time series of vertical eddy viscosities at a depth of 10 m from surface in stratified and non-stratified scenarios for points P1, P2, and P3 over Louisiana shelf. Fig. 6. Comparison of time series of simulated surface current velocities in stratified and non-stratified scenarios for points P1, P2, and P3 over Louisiana shelf.

substantially smaller than for the non-stratified scenario before the peak. The peak value of vertical eddy viscosity for the stratified scenario is almost half of what it is for the nonstratified scenario and occurs about three hours after that of the eddy viscosity peak for the non-stratified scenario. After the peak of vertical eddy viscosity for the stratified scenario is reached, eddy viscosities for the two simulation scenarios match well, presumably because the hurricane-induced mixing produces identical stability values across the water column for both scenarios. Simulated currents in the two scenarios at point P3 agree very well. This point is located about 10 km (about 0.28 RMW) from the right side of the hurricane's track. This point is located in the area that is confined by the Bird's Foot Delta and is affected by the rightward bias of the

hurricane's wind. Hence, it is expected that high current speeds are produced over this area, and the associated mixing is much stronger than it is at points P1 and P2. With the substantial mixing in this area, the calculated vertical eddy viscosities for both stratified and non-stratified scenarios should be similar. As Fig. 7(c) illustrates, time series of estimated vertical eddy viscosities are almost the same for both scenarios. Similar values of vertical eddy viscosity maintained similar amounts of turbulent energy across the water column, leading to similar surface currents (Fig. 6(c)). The difference between the shelf currents for the stratified and non-stratified scenarios was also investigated by examining current variations for three cross-sections, including the north-south sections A and B and the east-west section 1 (see Fig. 2 for locations). During the several hours that Katrina was approaching the shelf and passing over it, currents had a strong cross-shelf component (for example, Fig. 5), so only the northsouth current component is shown in Fig. 8, where the arrows

Please cite this article in press as: Allahdadi, M.N., Li, C., Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina, Water Science and Engineering (2017), http://dx.doi.org/10.1016/j.wse.2017.03.012

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represent the overall current directions in upper and lower layers across the water column. Locations of sections A and B are selected to present the patterns of stratified and nonstratified shelf areas during the hurricane, respectively. For section A, located south of Terrebonne Bay, the distance to Katrina's track is about 100 km (2.8 RMW). At this

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location, hurricane-induced mixing is weak, and the water column is significantly stratified (Allahdadi, 2014). The pattern of the north-south component of currents across this section for the two simulation scenarios is compared at the time when Katrina's eye was located at the Southwest Pass, in Fig. 8(a) and (b). Although over the offshore part of sections

Fig. 8. Contours of simulated cross-shelf currents at 10:00 UTC on August 25, 2005 across north-south and east-west sections for stratified and non-stratified scenarios. Please cite this article in press as: Allahdadi, M.N., Li, C., Effect of stratification on current hydrodynamics over Louisiana shelf during Hurricane Katrina, Water Science and Engineering (2017), http://dx.doi.org/10.1016/j.wse.2017.03.012

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there are some similarities, some significant differences are noticeable over the inner-shelf area. A well-developed twolayer current with the surface layer flowing away from the shore and the lower layer flowing shoreward is depicted in the non-stratified scenario, while there is more variability of currents across the water column for the stratified scenario. An approximately uniform current, especially for the lower layer, is produced in the non-stratified scenario. For the stratified scenario, the simulated current pattern across the lower layer, particularly over the middle part of section A (a cross-shore distance of 20e40 km in Fig. 8(a)) is more complex. Over the middle cross-section region and beneath the water depth of 10 m, a rectangular zone with a relative high-velocity core is formed. For section B, located about 10 km from the right side of the Katrina's track (about 0.28 RMW), simulated current patterns in the two scenarios are more similar (Fig. 8(c) and (d)). The results for both scenarios show well-developed twolayer circulations. The upper layer flows shoreward under the effect of southerly hurricane winds on the right side of Katrina's track. At the same time, compensatory currents running away from the shore are produced in the lower layer (lower than the mid-depth). Current patterns across both layers are similar for the two scenarios. However, more variability occurs in the stratified scenario. The vertical structure of the simulated current was also investigated for an east-west section (section 1 in Fig. 2), extending westward from the Southwest Pass. Like north-south sections, variations of crossshelf current for section 1 at the time when the eye was located at the Southwest Pass are presented in Fig. 8(e) and (f), where the dashed line shows the location of the hurricane's eye at this time. Current patterns demonstrate similar two-layer flow systems, as illustrated for north-south sections. For the upper layer, the current direction is mainly away from the shore (negative velocities) at the left side of the hurricane's eye. Current patterns for the two simulation scenarios are similar for the areas closer to the hurricane's track. Significant differences are identified for areas further to the west. These remote areas exhibit more oscillatory current patterns and more variability across the water column. 4. Discussion Simulation results of Louisiana shelf currents for stratified and non-stratified scenarios during Hurricane Katrina show that current patterns and values can be either similar or highly different, depending on the simulated location with respect to the hurricane's eye at a specific time. It is inferred that, for areas close to the eye, especially on the right side of Katrina's track, the results from the two simulation scenarios were consistent, while differences were more pronounced as the distance from the eye (in this case to the west) increased. This is consistent with the modeling study of Keen and Glenn (1999) for currents induced by Hurricane Andrew over the Louisiana shelf. In their study, for areas within 1 RMW of the hurricane center, where the turbulent mixing was strong, with significant mixing occurring across the water column, similar currents were simulated in the stratified and non-stratified scenarios, and the simulated results were

Fig. 9. Difference between average simulated surface currents in two simulation scenarios over Louisiana shelf and corresponding average mixed layer depths in meters.

consistent with the measurements. For areas farther than 2.5 RMW from the hurricane center, turbulent mixing was weak. Hence, differences in simulated currents between the two scenarios were large, and the measured currents cannot be reproduced in the non-stratified scenario. This conclusion is illustrated in Fig. 9, where the solid line shows the hurricane's track. Fig. 9(a) shows the difference (Dc) between average simulated surface currents for 20 h (from when hurricane wind started to affect the shelf until several hours after the landfall) in the two simulation scenarios across the study area. For the sake of convenience, a dashed circle depicting the area 1 RMW from the hurricane center (1 RMW zone), when the eye was located west of the Southwest Pass, is sketched. As expected, for the area that was affected by hurricane wind within the 1 RMW zone, the difference in simulated currents between the two scenarios is generally small. The maximum differences are observed in the area located in the south of Terrebonne Bay. The closest distance of this area to the average eye location is about 1.8 RMW, while the farthest point is about 3 RMW from the hurricane center. Different responses of simulated currents regarding the distance from the hurricane center and the intensity of turbulent mixing can be justified based on the mixing characteristics of the shelf during Katrina. Fig. 9(b) shows the average mixed layer depth (MLD) over the shelf during the time Katrina affected the shelf (the averaging period is consistent with Fig. 9(a)). Over the

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shelf, the greatest values of the MLD were found within the 1 RMW zone. This area corresponds to the small values of the difference between the simulated currents for two simulated scenarios. The general decline of the mixing strength in the west and the area off Terrebonne Bay (shown as lesser mixing depth in Fig. 9(b)) coincides with the increase of difference between simulated currents for two scenarios. The higher values of differences right at the northwest of the Southwest Pass are consistent with the decrease in the mixed layer depth in the vicinity of the delta as a result of Southwest Pass geometry blocking northward currents. The effect of stratification on the momentum balance and the role of vertical eddy viscosity in controlling stratification is described in Eqs. (1) and (2). According to these equations, the conclusion above implies that, over the areas that show larger differences between simulated currents in the stratified and non-stratified water columns, corresponding values for the vertical eddy viscosity should be substantially different (also illustrated in Fig. 7 for point P1). This is basically due to the different behaviors of turbulence in stratified and nonstratified flows (Dickey and Mellor, 1980). Based on laboratory experiments, Dickey and Mellor (1980) found that the decay of turbulent energy is similar in stratified and nonstratified waters until the Richardson number decreases to a critical value. At this time, turbulent decay ceases abruptly and then continues with a much lower rate, as compared to the time before the critical stage. At this new stage, internal gravity waves are dominant. Including the effect of stratification in turbulent closure algorithms like Mellor-Yamada level 2.5, which calculates vertical eddy viscosity in the model, has always been a challenge (Galperin et al., 1988; Kantha and Clayson, 1994). In the original Mellor-Yamada turbulent closure model (Mellor and Yamada, 1974, 1982), one of the main problems was insufficient turbulent mixing for Richardson numbers larger than a typical value like 0.21 (Kantha and Clayson, 1994; Burchard and Baumert, 1995). Durski et al. (2004) used two different closure models, including Mellor-Yamada level 2.5 and the enhanced version of K-profile parameterization (KPP) to study turbulent mixing and circulation, over an idealized continental shelf area. They concluded that the selected closure model and the initial stratification could significantly alter the coastal circulation. The inconsistency was highly reduced by parameterization of the stability function Sm , as suggested by Kantha and Clayson (1994) and Galperin et al. (1988). As illustrated in Eq. (3), the stability function is used to calculate the vertical eddy viscosity based on turbulent energy and the turbulent macroscale. The modified equation used in FVCOM for estimating the stability function is (Chen et al., 2006)

Sm ¼

0:4275  3:354Gh ð1  34:676Gh Þð1  6:127Gh Þ

ð5Þ

where Gh is the gradient Richardson number calculated as follows:

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Fig. 10. Time series of gradient Richardson number for three different locations.

Gh ¼

l2 grz q2 r0

ð6Þ

where g is the acceleration due to gravity, r0 is the reference water density, and rz is the water density at vertical coordinate z. Galperin et al. (1988) assigned an upper value of 0.023 for Gh , representing the case of unstable stratification (rz > 0) and a lower bond value of 0.28 for the stable stratification case (rz < 0). Time series of the gradient Richardson number at middepths for points P1, P2, and P3 are shown in Fig. 10. At points P1 and P2, the gradient Richardson number approaches zero only for several hours before and after the time the eye reaches the Southwest Pass (t ¼ 0). At point P3, it reaches zero at t ¼ 10 h and remains close to zero for at least the next 60 h. The calculated results of shelf-wide vertical eddy viscosity for both the stratified and non-stratified scenarios across an east-west section (section 1 in Fig. 2), along with the variations of water temperature (temperature resulting from the simulation for a stratified water column) are presented in Fig. 11. Note that variations of water salinity across the water column for each scenario followed patterns similar to the temperature and therefore were not shown here. Examining simulated vertical eddy viscosity and temperature across this section demonstrates the effect of stratification/Richardson number on estimating the vertical eddy viscosity. Profiles are presented for 10:00 UTC on August 29, 2005 in Fig. 11, while the eye was located just west of the Southwest Pass. Although there are similarities between the calculated eddy viscosities in the stratified and non-stratified scenarios in terms of area and depths of influences, some remarkable differences are also observed. As illustrated in Fig. 11(a) and (b), over the mixed

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5. Summary and conclusions

Fig. 11. Variations of calculated vertical eddy viscosity across section 1 at 10:00 UTC on August 29, 2005 in stratified and non-stratified scenarios and corresponding variations of simulated water temperature in stratified scenario.

area located on the right side of Katrina's track (very right corner of the shown profile), the calculated eddy viscosities are almost identical, both in values and pattern. Over the other parts of the shelf, the differences are more noticeable. A smoothed pattern is simulated for the non-stratified scenario, while many oscillations and irregularities are observed for the stratified scenario. The oscillation is presumably produced by the internal waves, as a result of the interaction between the turbulence and the stratified flow as mentioned by Dickey and Mellor (1980). Development of a mixed layer across the water column over the areas within 1 RMW of the hurricane center (Fig. 11(c)) is consistent with the zone associated with smaller differences between the simulated currents in two scenarios as illustrated in Fig. 9(a). As expected, the layer of high turbulent mixing was interrupted by temperature oscillations at the base of the mixed layer. This behavior is consistent with modeling results of Elsberry et al. (1976).

In this study, the effect of stratification on the current hydrodynamics was examined through numerical simulations of the Louisiana shelf circulation under Hurricane Katrina. Two simulation scenarios, including an initially stratified shelf and an initially non-stratified shelf, were examined using FVCOM. The different behaviors of vertical eddy viscosity for the two simulation scenarios were addressed based on the differences of turbulent decay in stratified and non-stratified flows. The Mellor-Yamada level 2.5 turbulent closure model and the associated modifications applied by Galperin et al. (1988) and Kantha and Clayson (1994) were incorporated in FVCOM, as an appropriate approach to parameterizing vertical eddy viscosity. The parameterization considers the effect of the gradient Richardson number on the stability function, which is applied to the estimation of vertical eddy viscosity. The dependency of vertical eddy viscosity on the gradient Richardson number was demonstrated by examining values of the parameter for locations with different stratification conditions. The following conclusions are drawn: (1) Model results showed that circulation patterns under the two scenarios were generally similar. However, some noticeable differences were identified. Over the mixed area, especially on the right side of Katrina's track, the differences were small, while over the stratified area on the left side (the area located outside of the 1 RMW zone, which was far from the intense hurricane-induced turbulence), the differences were conspicuously larger. Examining the simulated cross-shelf velocities across north-south and east-west sections confirmed this conclusion. Furthermore, comparison of the calculated vertical viscosities for the stratified and non-stratified scenarios for three points of different locations with respect to the hurricane center strongly supported this conclusion. (2) Stratification modulates the vertical eddy viscosity that directly affects the current through a term in the momentum equations. Hence, treatment of vertical eddy viscosity is of great importance in circulation modeling. The parameterization of vertical eddy viscosity is based on the particular behavior of turbulence in stratified flow, which is similar to that of non-stratified flow until it reaches a critical gradient Richardson number. (3) The results of the present study demonstrate that the effect of stratification on the 3D baroclinic modeling of shelf waters may not be neglected and, to achieve high-accuracy results for circulation, stratification and its associated parameters should be treated appropriately. In this regard, there are two key aspects: First, the initial fields of temperature and salinity that specify the stratification condition at the beginning of simulation should be provided based on reliable data. Lack of appropriate data indicating the initial stratification can degrade the accuracy, even when compared to the more unrealistic non-stratified scenario (Keen and Glenn, 1999). Second, suitable turbulent closure models should be applied for resolving the vertical eddy viscosity. Although the MellorYamada level 2.5 is a widely used model, the performance of other models, including K-profile parameterization (KPP)

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and the k-3 model, can be examined in order to determine the best approach (Li et al., 2005). However, some parameters, including the background eddy viscosity and B1 (for MellorYamada level 2.5), should be tuned using the available hydrodynamics data across the water column. Acknowledgements The authors would like to thank Dr. Chang-sheng Chen (University of Massachusetts-Dartmouth) for his kindness in sharing the FVCOM code. References Allahdadi, M.N., Jose, F., Stone, G.W., D'Sa, E.J., 2011. The fate of sediment plumes discharged from the Mississippi and Atchafalaya rivers: An integrated observation and modeling study for the Louisiana Shelf, USA. In: Proceedings of the Coastal Sediments. World Scientific, Miami, pp. 2212e2225. Allahdadi, M.N., Jose, F., Patin, C., 2013. Seasonal hydrodynamics along the Louisiana Coast: Implications for hypoxia spreading. J. Coast. Res. 29(5), 1092e1100. http://dx.doi.org/10.2112/JCOASTRES-D-11-00122.1. Allahdadi, M.N., 2014. Numerical Experiments of Hurricane Impact on Vertical Mixing and De-stratification of the Louisiana Shelf Waters. Ph. D. Dissertation. Louisiana State University, Baton Rouge. Allahdadi, M.N., Jose, F., D'Sa, E.J., Ko, D.S., 2017. Effect of wind, river discharge, and outer-shelf phenomena on circulation dynamics of the Atchafalaya Bay and shelf. Ocean Eng. 129, 567e580. http://dx.doi.org/ 10.1016/j.oceaneng.2016.10.035. Allahdadi, M.N., Li, C., 2017. Numerical simulation of Louisiana shelf circulation under Hurricane Katrina. J. Coast. Res. http://dx.doi.org/10.2112/ JCOASTRES-D-16-00129.1. Burchard, H., Baumert, H., 1995. On the performance of a mixed-layer model based on the k-ε turbulence closure. J. Geophys. Res. Oceans 100(C5), 8523e8540. http://dx.doi.org/10.1029/94JC03229. Chaichitehrani, N., 2012. Investigation of Colored Dissolved Organic Matter and Dissolved Organic Carbon Using Combination of Ocean Color Data and Numerical Model in the Northern Gulf of Mexico. M. E. Dissertation. Louisiana State University, Baton Rouge. Chaichitehrani, N., D'Sa, E.J., Ko, D.S., Walker, N.D., Osburn, C.L., Chen, R.F., 2014. Colored dissolved organic matter dynamics in the Northern Gulf of Mexico from ocean color and numerical model results. J. Coast. Res. 30(4), 800e814. http://dx.doi.org/10.2112/JCOASTRES-D-13-00036.1. Chen, C.S., Xie, L.S., 1997. A numerical study of wind-induced, near-inertial oscillations over the Texas-Louisiana shelf. J. Geophys. Res. Oceans 102(C7), 15583e15593. http://dx.doi.org/10.1029/97JC00228. Chen, C.S., Beardsley, R.C., Franks, P.J.S., Van Keuen, J., 2003. Influence of diurnal heating on stratification and residual circulation of Georges Bank. J. Geophys. Res. Oceans 108(C11), GL09.1eGL09.21. Chen, C.S., Beardsley, R.C., Cowles, G., 2006. An Unstructured Grid, FiniteVolume Coastal Ocean Model FVCOM User Manual. University of Massachusetts-Dartmouth, New Bedford. Cooper, C., Thompson, J.D., 1989. Hurricane-generated currents on the outer continental shelf, 1: Model formulation and verification. J. Geophys. Res. Oceans 94(C9), 12513e12539. http://dx.doi.org/10.1029/JC094iC09p12513. Csanady, G.T., 1972. Response of large stratified lakes to wind. J. Phys. Oceanogr. 2(1), 3e13. http://dx.doi.org/10.1175/11520-04/1520-0485(1972)002 <0003:ROLSLT>2.0.CO;2. Davies, A.M., 1985. A three-dimensional modal model of wind induced flow in a sea region. Prog. Oceanogr. 15(2), 71e128. http://dx.doi.org/10.1016/ 0079-6611(85)90032-1. Dickey, T.D., Mellor, G.L., 1980. Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99(1), 13e31.

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