Boussinesq modeling of longshore currents

A time domain Boussinesq model for nearshore hydrodynamics is improved to obtain the conservation of vertical vorticity correct to second order and extended for use on an open coast using longshore periodic boundary conditions. The model is utilized to simulate surface waves and longshore currents under laboratory and field conditions. Satisfactory agreement is found between numerical results and measurements, including root mean square wave height, mean water level, and longshore current. One striking result of the simulations is the prediction of the strong longshore current in the trough shoreward of the bar as observed during the Duck Experiment on Low‐frequency and Incident‐band Longshore and Across‐shore Hydrodynamics field campaign. The model results give insight into the spatial and temporal variability of wave‐driven longshore currents and the associated vertical vorticity field under the phase‐resolving, random wave forcing with wave/current interaction. Numerical experiments are carried out to examine the response of the modeled longshore currents to the randomness of surface waves and the cross‐shore distributions of bed shear stress coefficient. We find that both regular and irregular waves lead to very similar mean longshore currents, while the input of monochromatic, unidirectional waves results in much more energetic shear waves than does the input of random waves. The model results favor Whitford and Thornton 's 1996 finding that the bed shear stress coefficient for the area offshore the bar is larger than that in the trough, as better agreement with the field data for both regular and irregular waves is found if such coefficients are used in the Boussinesq model.