A Coupled Hydrodynamic-Wave Model for Simulating ...

In Estuarine and Coastal Modeling, Proceedings of the 7th International Conference, Malcolm L. Spaulding, ed., ASCE, Reston, VA, pp. 725-744, 2002.

A Coupled Hydrodynamic-Wave Model for Simulating Wave and Tidally- Driven 2D Circulation in Inlets Mark Cobb1 and Cheryl Ann Blain2 Abstract This study focuses on modeling the 2D, depth-averaged circulation of an ideal inlet that is driven by waves and tides using a coupled hydrodynamic-wave model. The circulation of an ideal inlet, consisting of a shallow bay of constant depth connected by a relatively narrow inlet to a sloping coastal shelf region, is studied. Circulation within the inlet is examined during the flood, slack, and ebb phases of the tidal cycle. The ideal inlet is also simulated with only wave forcing to better understand the effect of wave-current interaction on the circulation. The influence of the various forcings on bay/inlet circulation is further investigated by the introduction of Lagrangian tracers. Wave-current interaction is simulated by iteratively coupling the depthintegrated ADCIRC-2DDI hydrodynamic model to the 2D phase-averaged spectral wave model SWAN. ADCIRC-2DDI is a fully developed, 2-dimensional, finite element, barotropic hydrodynamic model capable of including wind, wave, and tidal forcing as well as river flux into the domain. The iterative hydrodynamicwave model coupling is captured through the following approach. First, radiation stress gradients, determined from the SWAN wave field, serve as a surface stress forcing for ADCIRC. Elevations and currents, computed from ADCIRC, are subsequently input into the SWAN model at each iteration. The surface stress is then recalculated using the new wave field. Between these iterations the ADCIRC model is run for some appropriately small time interval during which the wave field is held constant. 1

Sverdrup Technology, Inc. (ASGMS), MSAAP Building 9101, Door 136, Stennis Space Center, MS 39529, USA, Tel: 228-689-8541, E-mail: [email protected] 2 Oceanography Division (Code 7322), Naval Research Laboratory, Stennis Space Center, MS 39529-5004, Tel: 228-6885450, E-mail: [email protected]

1 Mark Cobb and Cheryl Ann Blain


Introduction Bays and inlets are important areas from both a biological and economic standpoint. Many species depend on these coastal environments for survival and this has a direct impact on the economic well being of the surrounding area. In addition, bays and inlets are also important areas of sediment and pollutant transport. In order to protect as well as develop these areas, a better understanding of their circulation patterns and the forces that drive them is essential. Tides are one of the primary forcing mechanisms that drive the circulation of these coastal environments. Waves can also be another significant forcing mechanism of coastal circulation and wave-current interaction is essential for capturing the combined effect of tidal and wave forcing in an inlet/bay system. Although wind is an important forcing mechanism of the circulation as well, the focus of this study is on forcing mechanisms that couple to each other. In this study the effects of wave-current interaction on wave and wave-tide driven circulation within bays and at the entrance to embayments are investigated using a coupled hydrodynamic-wave model. An iterative coupled hydrodynamicwave model has been developed using the depthintegrated ADCIRC-2DDI finite element hydrodynamic model and the 2D spectral SWAN wave model for simulating wave-current interaction in a tidal inlet. The exact details of this approach will be discussed later in the paper. An idealized domain geometry, used in previous studies by Kapolnai et al. (1996) and Veeramony and Blain (2001), is employed for this study. This ideal domain consists of an inner basin (or embayment) connected to an outer ocean basin by a narrow inlet. The previous studies that used this inlet geometry examined tidal, wind, and river forced circulation. In this study two principle cases are examined 1) the uncoupled and coupled waveinduced circulation and 2) the coupled wave-tide forced circulation. The wave fields, surface elevations, and current velocity vectors as well as the motion of passive Lagrangian tracers are examined in order to characterize the influence of the different forcing mechanisms and the effects of wave-current interaction on the circulation. Circulation and Wave Models Sea surface elevation and coastal currents are modeled using the fully nonlinear, two-dimensional, barotropic hydrodynamic model ADCIRC-2DDI. The ADCIRC (ADvanced CIRCulation Model for Shelves, Coasts and Estuaries) model, developed by Luettich et al. (1992) and Westerink et al. (1994a), has a successful history of tidal and storm surge prediction in coastal waters and marginal seas (e.g. Blain et al., 1994; Kolar et al., 1994; Westerink et al., 1994b; Blain et al., 1998). The depthintegrated shallow water equations, derived through 2 Mark Cobb and Cheryl Ann Blain


vertical integration of the three-dimensional mass and moment um balance equations subject to the hydrostatic assumption and the Boussinesq approximation, form the basis of the ADCIRC-2DDI model (Note: 2DDI stands for two dimensional depthintegrated). A spatially variable surface stress forcing is determined from the radiation stress (Sxx, Syy, Sxy, Syx) gradients of the wave field (Longuet-Higgins and Stewart, 1964) obtained from the SWAN wave model. The simplified non-conservative primitive equations are ∂ζ + ∇ xy ⋅ ( H ν ) = 0 ∂t

(1)

M xy τ sxy τ bxy ∂ν + ν ⋅ ∇ xyν + f ×ν = −∇ xy ( gζ ) + + − ∂t H ρ0 H ρ 0 H ∂S   ∂S τ sx = −  xx + yx  ∂y   ∂x ∂S   ∂S τ sy = −  yy + xy  ∂x   ∂y

( 2) (3) ( 4)

where t represents time, x,y are the Cartesian coordinate directions, ζ is the free surface eleva tion relative to the geoid, ν is the depth-averaged horizontal velocity vector, H = ζ + h is the total water column depth, h is the bathymetric depth relative to the geoid, f (= 2Osin(?), where O is the angular frequency of rotation for the earth and ? is the degrees of latitude) is the coriolis parameter, g is the acceleration due to gravity, ρ0 is the reference density of water, Mxy is the horizontal momentum diffusion/dispersion, τsx and τsy are the applied horizontal free surface stresses, and τbxy is the horizontal bottom stress vector. This set of equations is considered to be time-averaged over a wave period. Bottom stress terms are parameterized using the standard no nlinear quadratic friction law:

(

τ bxy = C f ρ0 U 2 + V 2

)

1/ 2

ν

(5)

where Cf is the nonlinear bottom friction coefficient. The lateral mixing due to diffusion/dispersion is:

(

M xy = Eh ∇ 2xy ( Hν )

)

( 6)

where Eh is the horizontal eddy viscosity coefficient for momentum diffusion/dispersion (Kolar and Gray, 1990). 3 Mark Cobb and Cheryl Ann Blain


The wave field used to force the ADCIRC-2DDI model is derived from the 2D multi-spectral SWAN wave model (Booij et al., 1999). The SWAN wave model is based on the wave action balance equation and can simulate wave refraction, shoaling, blocking, and reflection due to bathymetry, sea surface elevations, and currents. SWAN also has the capability of using sea surface elevations and currents as input for the calculation of the wave field. It should be noted tha t SWAN cannot simulate wave diffraction and therefore its results in regions where diffraction is significant (e.g. an obstacle) will not be accurate. For this initial study SWAN is a suitable wave model. The significance of diffractive effects in the ideal inlet will be investigated in a future study using a different wave model. An additional reason for using SWAN is its ability to model domains with complex coastlines, something which can be significantly more difficult (or impossible) with other wave models. Methodology of Wave-Current Interaction Wave-current (w-c) interaction is incorporated into the simulation by iteratively coupling ADCIRC and SWAN. Wave heights and directions computed by the SWAN wave model are interpolated onto the comput ational nodes of the finite element grid and radiation stress gradients are then determined at each node. The radiation stress gradients are the surface stress forcing for ADCIRC. It should be pointed out that the radiation stress is determined on the finite element grid using the peak frequency of the wave frequency spectrum, thus treating the SWAN wave data as monochromatic. The wave frequency spectrum is chosen to be quite narrow in order for this approach to produce reasonable results. This is not a restriction of the method but a simplification made for the application here. For the purpose of this study it is an acceptable approximation. In future studies that apply the model to real inlet/bay systems, a more sophisticated approach will be used to capture the full spectral features of the SWAN wave field. The sea surface elevations and currents of ADCIRC-2DDI are used by SWAN to compute a new wave field at each iteration, which is then used to recalculate the nodal radiation stress gradients. The ADCIRC model is initially run without two-way coupling for a time interval sufficient to obtain a steady state circulation. After this initial spin- up period, two-way coupling is activated and ADCIRC is run forward for a brief time interval, driven by a new static wave field. At the beginning of every iteration SWAN computes a new wave field that incorporates the ADCIRC sea surface elevation and current velocities from the last time step of the previous iteration (or spin-up). The ADCIRC simulation proceeds as before, forced by a new radiation stress field. This process is repeated after every iteration interval. Although it is possible to couple ADCIRC and SWAN at every time step, it is computationally too expensive to do so at the present time. 4 Mark Cobb and Cheryl Ann Blain


ADCIRC Domain The ideal tidal inlet (Figure 1) used in this study is taken from the work of Kapolnai et al. (1996). The computational domain consists of an inner basin (or embayment) (20 km by 10 km) connected to an outer ocean basin (49 km by 20 km) on the continental shelf through a narrow inlet (2 km by 3 km). The bathymetry changes linearly from an offshore depth of 14 m to 5 m at the mouth of the inlet. Beyond the mouth of the inlet the depth is held constant at 5 m. The resolution of the irregular finite element (FE) mesh is 125 m in the inlet and 1000 m throughout the rest of the domain. In addition, there is increased grid resolution at the mouth and exit of the inlet where the land boundaries are curved. In order to model the complex circulation in and around the inlet, increased resolution of the grid in this region is required. It was determined in a previous study by Veeramony and Blain (2001) that this finite element mesh resolution was sufficient to produce realistic circulation under tidal forcing.

Figure 1. Ideal inlet/bay computational domain. The southern boundary has an elevation specified boundary condition. 5 Mark Cobb and Cheryl Ann Blain


The boundaries of the ADCIRC domain are closed (a no flow condition is imposed which allows for lateral slip) except for the offshore ocean boundary. Two different boundary conditions are applied to this boundary depending on the type of simulation. If the circulation is forced only by waves, a zero elevation boundary condition is enforced along this boundary to simulate an unperturbed sea surface (in this region wave induced set-up/set-down should not be significant). When the circulation is forced with both waves and tides the offshore boundary elevation is modulated with specified tidal amplitudes that have zero phase at the boundary. SWAN Domain A regular finite difference (FD) grid of resolution of 125 m in the x and y directions is employed for the SWAN computational domain. This resolution is chosen so that the FD and FE grids have the same resolution throughout the inlet region where the wave and circulation fields change significantly over relatively small distances. The rectangular dimensions of the FD grid encompass the ADCIRC FE grid and normally incident waves propagate inward from the offshore ocean boundary. SWAN allows the user to specify barriers and their transmission coefficients for the purpose of limiting wave propagation into specified regions of the computational domain. For this application, barriers with zero transmission coefficients (and no reflection) are used to prevent waves from propagating outside the boundaries of the FE grid. These barriers start at the top corners of the ocean basin and continue to the top corners of the embayment along the boundaries of the FE grid. The lateral sides of the outer basin and the top boundary of the embayment are not closed, allowing waves to propagate out of the domain (but not into the domain). The SWAN barriers match the ADCIRC domain boundaries except where the ADCIRC grid boundaries curve at the junc tion of the inlet and the embayment and the junction of the inlet and the ocean. At these four locations the SWAN barriers form corners that are contained within the ADCIRC domain, leading to waves that decay quite rapidly within the ADCIRC domain. The result is large radiation stress gradients that would normally be present much closer to the boundaries of the ADCIRC grid if the SWAN barriers exactly followed the ADCIRC boundary. For the purposes of this study it is not necessary to improve upon this situation, although in future studies this issue will be resolved in a more realistic manner. Simulation Parameters i) Wave parameters 6 Mark Cobb and Cheryl Ann Blain


The incident wave field has a peak period of 10 seconds and significant wave amplitude of 0.5 m. These parameter values are considered appropriate for coastal wave conditions. The peak incident wave direction is specified as 90o since the waves enter perpendicular to the southern boundary of the domain. The default JONSWAP spectrum of the model (Booij et al., 1999) is used to specify the initial shape of wave spectrum at the boundary. A value of 20 is chosen for the gamma parameter in order to make the spectrum sharply peaked. ii) ADCIRC parameters A time step of 8 seconds is chosen for the ADCIRC simulations in order to satisfy the Courant condition (Westerink et al., 1994a). The lateral mixing (Eh ) and nonlinear bottom friction coefficient (Cf) are chosen to be 1.0 m2 /s and 0.0025 respectively. The value of Eh was determined in a previous study to be large enough to prevent the formation of instabilities in the circulation without significantly altering its elevation and velocity values (Veeramony and Blain, 2001). For simulations that involve tidal forcing a M2 tide with an amplitude of 0.15 m and a phase of zero at the southern boundary is used. The coriolis parameter has a value of .00008 which corresponds approximately to the northern Gulf of Mexico. Wave-Forced Circulation A coupled simulation with only wave forcing is performed to determine the general features of waveinduced circulation. An uncoupled “spin- up” simulation is run for 0.8 days until a steady state is reached. The coupled simulation is then run for an additional 0.24 days (or approximately 6 hours). The length of time between each coupled iteration is 0.02 days (or about 30 minutes). Reducing the iteration time to 0.01 days was found to have very little effect on the overall behavior of the circulation. A more thorough sensitivity study is required to characterize the effects of reducing the length of time between iterations. It should be noted that when comparisons are made between the uncoupled and coupled cases in this section, the data for the uncoupled and coupled cases are taken at 0.8 and 1.04 days respectively. In Figure 2 the sea surface elevation and the wave height are shown for the uncoupled and coupled simulations along a transect aligned with the inlet axis (ydirection) located at x=25,000 m.



Figure 2. Transects of (A) sea surface elevation (m) and (B) wave height (m) for uncoupled and coupled simulations that span the length of the domain along the inlet axis in the y direction (located at x=25,000 m). The wave transects in Figure 2B clearly show that the wave heights are decreasing within or close to the inlet region (y=19,000 to 24,000 m). This is due to directional spreading of wave energy, not depth- induced breaking. When the waves are coupled to the currents the peak of the wave height increases and becomes much sharper. The position of the peak also moves further offshore towards the inlet entrance. This indicates that the w-c interaction causes the waves to shoal earlier then they normally would because of an opposing current at the mouth of the inlet. It is apparent from Figure 2A that currentinduced changes in the wave field produce a significantly different wave- forcing field. The waveinduced set-down in Figure 2A is greater with w-c interaction and the waveinduced set- up is steeper than the non w-c case in the vicinity of the inlet. In order to understand the influence of the currents on the wave field a comparison is made between the wave fields with and without w-c interaction in Figure 3. It is apparent from Figure 3 that w-c interaction significantly alters the wave height field throughout the inlet and into the embayment. In particular there is a sharp peak in the wave height near the left corner of the inlet mouth, making the wave field highly asymmetric. It will be shown later this that this peak corresponds to a strong current flowing out of the inlet that causes the incoming waves to shoal. 8 Mark Cobb and Cheryl Ann Blain


Figure 3. Contour plots of the wave height (m) field for the uncoupled (left) and coupled (right) simulations. The contour increments are 0.057 m. For the uncoupled case the wave height minimum and maximum are 0.0 and 1.18 m respectively. For the coupled case the wave height minimum and maximum are 0.0 and 1.5 m respectively. Wave-current interaction (as seen from Figure 3) also results in an increase in the directional spreading of wave energy, caus ing the wave field to spread out into the bay. This is consistent with the more rapid decrease in wave height seen in Figure 2B and in contrast to the uncoupled case in which the waves are more narrowly focused as they travel into the bay. In Figure 4 the uncoupled and coupled sea surface elevations are shown. In both cases the waves create significant set-down at the corners of the inlet mouth where they are forced to zero by the barriers that define the SWAN grid. In the coupled case there is a significant asymmetry in the set-down at these locations due to w-c interaction. The out-flowing current seen in Figure 5 is responsible for this asymmetry through its effect on the wave field (Figure 3), as mentioned previously. Within the bay, the wave forcing creates a narrow region in which the sea surface elevation is lower than the surrounding water level (Figure 4). Because the waves are spreading outward from the inlet exit the total wave forcing is not 9 Mark Cobb and Cheryl Ann Blain


Figure 4. Uncoupled (left) and coupled (right) sea surface elevation (m) contours for the wave-driven circulation. The elevation contours are in increments of 0.002 m. balanced by elevation gradients alone. Thus, currents are generated by elevation gradients as well as surface wave stress. From Figure 2A it is also apparent that there is a large elevation gradient from the bay to the exit of the inlet. The overall cross-shore and alongshore elevation gradients force water to exit the bay along the axis of the inlet, as seen from circulation of the coupled run in Figure 5. It should also be pointed out that water is flowing into the bay along the left side of the inlet, forced by radiation stress gradients. In addition, a very strong outflowing current is seen in Figure 5 at the mouth of the inlet where a large waveinduced set-down is observed in Figure 4. This current is fed by waveinduced inflow at the corners of the inlet mouth as well as outflow from the bay. The maximum current velocity in this outflow is approximately 0.5 m/s. It is this strong opposing current that accounts for the change in wave height of the coupled case in Figure 2B.



Figure 5. Current velocity vectors (m/s) for the coupled wave-driven circulation at 1.04 days. A comparison of the uncoupled and coupled cases in Figure 6 shows how significantly w-c interaction can effect the inlet/bay circulation. The currentinduced changes in the wave field, as previously discussed, lead to a very strong current on the left side of the inlet mouth in contrast to the uncoupled case in which the outflow is essentially in the middle of the inlet. In addition, a large vortex is created by this current and the asymmetry of the circulation. It should also be pointed out that there are vortices at the corners of the inlet mouth in both cases that result in very complex circulation patterns. The wave field radiation stress gradients at the corners of the inlet mouth, previously mentioned in the SWAN Domain section, lead to the formation of these vortices through set- up/setdown and wave driven circulation. The asymmetry in the coupled circulation can be partly attributed to asymmetries in these vortices (and the wave field) in the uncoupled case. This asymmetry arises in part because SWAN does not produce exactly the same wave field at the corners of the inlet mouth and because the wave field must be interpolated beyond the SWAN domain. Further investigation is 11 Mark Cobb and Cheryl Ann Blain


Figure 6. Uncoupled (left) and coupled (right) wave-driven circulation current velocity vectors (m/s) at 0.8 and 1.04 days respectively. required to completely understand what is occurring in this region. This example clearly demonstrates the importance of incorporating w-c interaction into simulations where waves encounter opposing currents. Further investigation is required to determine if the coupled case ever reaches a quasisteady state over a longer period of time. Because the wave forcing changes after each iteration in the coupled case, it is not expected that a true steady state can ever be achieved. 12 Mark Cobb and Cheryl Ann Blain


Figure 7. Wave heights (m) for flood (solid), slack (dashed), ebb (long dashed), and no tides (circles) along a y-transect located at x=25,000 m. The wave heights for the coupled wave-driven flow at 1.04 days are used for the case without tides. Wave and Tide-Forced Circulation To examine w-c interaction effects in the presence of both tides and waves, a coupled simulation is run with a M2 tide of amplitude of 0.15 m at the open boundary and the same incident wave field used in the previous case of wavedriven circulation. An initial uncoupled spin- up phase of 6 days is used to initiate the coupled run. During the spin- up phase a constant wave- forcing field is applied. The coupled run then proceeds for an additional 0.52 days (12.48 hours) which is just a little longer then one M2 tidal cycle (12.42 days). The length of time between coupled iterations is 0.02 days as it was in the previous case. Because tidally- induced currents are much stronger than the waveinduced currents they alter the wave field to a much greater extent. In Figure 7 the wave heights are plotted along the same transect used for Figure 2 during the flood, slack, and ebb phases of the tide. For comparison the wave heights from the coupled case with only wave forcing are plotted as well in Figure 7. The wave heights during slack (proceeding to ebb) are quite similar to the wave only case as one might expect. The peak wave height for ebb is larger than slack and further offshore due to the larger opposing currents the waves encounter. The wave heights for flood (really the beginning of the flood phase) are not what one would normally expect. Instead of decreasing in magnitude and moving shoreward, the 13 Mark Cobb and Cheryl Ann Blain


Figure 8. Current velocity vectors (m/s) for the coupled wave-tide circulatio n during the flood phase of the M2 tide. peak wave height has become much more intense and moved further offshore. This occurs, as seen from Figure 8, because of an outflowing waveinduced current (starting at approximately x=25,000 m, y=20,000 m) that is fed by the incoming tidally-driven flood currents. As flood proceeds the tidal currents eventually overwhelm the waveinduced outflow and the waves decrease in magnitude and move shoreward. This illustrates the changes that can occur in tidally-driven circulation when waves are present. Because of the waveinduced circulation the tidally- induced currents and sea surface elevations will be altered during the flood, slack, and ebb phases of the tidal cycle. In Figure 9 the coupled wave-tide sea surface elevations are plotted against the M2 sea surface elevations at the same flood, slack, and ebb points in the tidal cycle along the same y-transect used for Figure 2 (x=25,000 m). It should be noted that these are the same flood, slack, and ebb points as those used for Figure 7. It is evident from Figure 9 that the waveinduced changes in the elevation are 14 Mark Cobb and Cheryl Ann Blain


Figure 9. Flood (top), slack (middle), and ebb (bottom) M2 tide (solid) and coupled wave-tide elevations (m) (dashed) along a y-transect located x=25,000 m. significant even in the presence of a strong tide. Overall, the coupled wave-tide elevation, during the three main phases of the tide, is lower than the M2 tidal elevation. The difference between the M2 and the coupled wave-tide sea surface elevations is about the same magnitude as the wave-induced set-down for the coupled wave-driven circulation in Figure 2A. During the flood and ebb phases of the tide the waveinduced set-up and set-down are clearly present in the elevation as evidenced by the slight ‘dip’ in the sea surface elevation around y=20,000 m. As previously seen in Figure 8 waveinduced circulation can significantly modify the tidally-driven currents. In Figure 10 the M2 tide and coupled wave-tide cross-shore velocities are compared at flood, slack, and ebb along the same ytransect used for Figure 9 (x=25,000). It is apparent from Figure 10 that the seaward wave-induced outflow at the mouth of the inlet, observed in the wavedriven circulation, is present throughout the tidal cycle. In particular, the magnitude of the outflowing current (approximately 0.25 - 0.7 m/s) is similar to the magnitude of the outflowing current in the wave-driven case (approximately 0.5 m/s). In addition, during flood and ebb the coupled wave-tide currents are significantly different from the M2 currents throughout the inlet. Examining the 15 Mark Cobb and Cheryl Ann Blain


Figure 10. Flood (top), slack (middle), and ebb (bottom) M2 tide (solid) and coupled wave-tide (dashed) cross-shore current velocities (m/s) along a y-transect located x=25,000 m. coupled wave-tide current velocity field at slack in Figure 11, it is easy to see that the outflow is being generated primarily by waveinduced inflow near the corners of the inlet mouth. Wave-driven currents entering the inlet encounter an elevation gradient (seen in figure 9B) which creates the outflowing current seen in Figure 11. The oscillations in the coupled wave-tide current at ebb (Figure 10C) are apparent as well in the current velocity vectors of Figure 12. The outflowing current slows in the middle of the inlet and then becomes increasingly negative as it is leaving. As a means to better understand the coupled wave-tide circulation passive Lagrangian tracers are used. The paths of these tracers can be calculated using time slices of the current velocity vectors (output every 72 seconds during the simulation) and from this information their final displacement can be determined. Sixteen tracers are positioned in a horizontal line at the entrance of the inlet (y=19,600) with 100 m intervals in the x-direction (starting at x=24,300). From Figure 13, in which the displacements of the tracers for the M2 tide and coupled wave-tide circulation are compared over 12.48 hours, the effects of wave forcing 16 Mark Cobb and Cheryl Ann Blain


Figure 11. Coupled wave-tide current velocity vectors (m/s) during the slack phase of the M2 tide.

Figure 12. Coupled wave-tide current velocity vectors (m/s) during the ebb phase of the M2 tide. 17 Mark Cobb and Cheryl Ann Blain


Figure 13. Displacement of passive Lagrangian tracers over a time period of 0.52 days (12.48 hours) for the M2 tide (left) and coupled wave-tide (right) simulations. Initial starting positions of the tracers are indicated by the horizontal row of stars at the mouth of the inlet. are apparent. Under the influence of the M2 tide the tracers essentially return to their initial positions. Although it should be noted that tidally- induced residual currents influence the motion of the tracers as well (Veeramony and Blain, 2001). In the coupled wave-tide case the tracers are dispersed into the inlet and the outer ocean basin because of waveinduced circulation at the mouth of the inlet (as seen in Figures 8, 11, and 12). This suggests that inlet and bay transport processes involving passive particles (such as fish larvae) could be significantly affected by incoming waves.



Conclusion The wave and wave-tide forced circulation of an ideal inlet has been examined using an iterative hydrodynamic-wave coupled model approach. It has been demonstrated that wave-current interaction is an important effect in the case of wave-driven circulation since incident waves encounter strong opposing currents (which are part of the waveinduced circulation). When coupled wavetide forcing is employed the wave field is affected to an even greater ext ent by tidally-driven currents in the vicinity of the inlet. Near the mouth of the inlet the waveinduced currents alter the M2 tidal currents quite significant ly, creating a significant outflowing current during the three main phases of the tidal cycle. Regardless of whether the circulation is forced by just waves or waves and tides, w-c interaction is found to play an important role in determining the overall circulation and wave- forcing field. It has also been demonstrated that waveinduced circulation and w-c interaction will significantly alter the transport of passive particles in tidally-driven inlets and bays. This suggests that it is important to understand the influence of wave forcing to the same extent as tidal forcing when investigating the transport of sediment, pollutants, and biological organisms in bays and inlets. References Blain, C. A., J. J. Westerink, and R. A. Luettich. (1994). “The influence of domain size on the response characteristics of a hurricane storm surge model.” J. Geophys. Res., 99, C9, 18467-18479. Blain, C. A., J. J. Westerink, and R. A. Luettich. (1998). “Grid convergence studies on the prediction of hurricane storm surge.” Int. J. Num. Methods Fluids, 26, 369401. Booij, N., R. C. Ris, and L. H. Holthuijsen. (1999). “A third- generation wave model for coastal regions, Part 1, Model description and validation.” J. Geophys. Res., 104, C4, 7649-7666. Kapolnai, A., F. E. Warner, and J.O. Blanton. (1996). “Circulation, Mixing, and Exchange Processes in the Vicinity of Tidal Inlets: A Numerical Study.” J. Geophys. Res.,101(C6), 14253-14268. Kolar, R. L. and W. G. Gray. (1990). “Shallow water modeling in small water bodies.” Proc. 8th Int. Conf. Comp. Meth. Water Res., Springer-Verlag, Berlin, 149-155. 19 Mark Cobb and Cheryl Ann Blain


Kolar, R. L., J. J. Westerink, M.E. Cantekin, and C. A. Blain. (1994). “Aspects of nonlinear simulations using shallow water models based on the wave continuity equation.” Computers and Fluids, 23, 523-538. Longuet-Higgins, M. S., and R. W. Stewart. (1964). “Radiation stresses in water waves; A physical discussion, with applications.” Deep Sea Research, Vol. 11, 529562. Luettich, R. A., J. J. Westerink, and N. W. Scheffner. (1992). “ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves, Coasts, and Estuaries, Report 1: Theory and Methodology of ADCIRC-2DDI and ADCIRC3DL.” Technical Report DRP-92-6, U.S. Army Corps of Engineers Waterways Experimental Station, Vicksburg, MS 137 pp. Westerink, J. J., C. A. Blain, R. A. Luettich, and N. W. Scheffner. (1994a). “ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves, Coasts, and Estuaries, Report 2: User’s Manual for ADCIRC-2DDI.” Technical Report DRP-92, Department of the Army. Westerink, J. J., R. A. Luettich, and J. C. Muccino. (1994b). “Modeling tides in the western north Atlantic using unstructured graded grids.” Tellus, 46A, 178-199. Veeramony, Jayaram, and Cheryl Ann Blain. (2001). “Barotropic Flow in the Vicinity of an Idealized Inlet – Simulations with the ADCIRC Model.” NRL/FR/7320-01-9977.
