Numerical Simulation of Spatial Lag Between Wave Breaking Point and Location of Maximum Wave-Induced Current

A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point. The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direc- tion. The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress. An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy. The wave driver model is a phase-averaged wave model based on the wave action balance equation. Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach am used to evaluate the model＇s performance. The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.

Three-dimensional numerical modeling of nearshore circulation

A three-dimensional nearshore circulation model was developed by coupling CH3D, a three-dimensional hydrodynamic model and REF/DIF, a nearshore wave transformation model. The model solves the three-dimensional wave-averaged equations of motion. Wave-induced effects on circulation were introduced in the form of radiation stresses, wave-induced mass transport, wave-induced enhancement of bottom friction and wave-induced turbulent mixing. Effects of breaking waves were considered following Svendsen (1984a and 1984b) and Stive and Wind (1986). The model was successfully tested against the analytical solution of longshore currents by Longuet and Higgins (1970). The model successfully simulated the undertow as observed in a laboratory experiment by Stive and Wind (1982). In addition, the model was applied to a physical model by Mory and Hamm (1997) and successfully reproduced the eddy behind a detached breakwater as well as the longshore current on the open beach and the contiguous eddy in the open area of the wave tank. While the qualitative agreement between model results and experimental observations was very good, the quantitative agreement needs to be further improved. Albeit difficult to explain every discrepancy between the model results and observations, in general, sources of errors are attributed to the lack of understanding and comprehensive description of following processes: (1)the horizontal and vertical distribution of radiation stress, especially for breaking waves;(2)the detailed structure of turbulence;(3)Wave-current interaction (not included at this moment); and (4)the wave-current boundary layer and the resulting bottom shear stress.

An Improved Nearshore Wave Breaking Model Based on the Fully Nonlinear Boussinesq Equations

This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.

Development of A Depth-Integrated Longshore Current Model with Unstructured Grids

A depth-integrated model for simulating wave-induced longshore current was developed with unstructured grids. Effects of surface roller and horizontal mixing under combined waves and currents were incorporated in the numerical model. Recommended values of model coefficients were also proposed based on sensitivity analysis. Field observations and three series of laboratory measurements including two cases conducted on the plane beach and one implemented on the ideal inlet were employed to examine the predictive capability of this model. For the field case and laboratory cases conducted on the plane beach, numerical results were compared favorably with the measured data. For the case with an ideal inlet, simulated circulation pattern is supposed to be reasonable although some deviations between numerical results and measured data still can be detected.