Effects of Cross-Shore Boundaries on Longshore Current Simulations

The paper analyzes how prescribed errors in the boundary conditions along both upstream and downstream cross-shore boundaries spread inside the computational domain. For simplicity we consider a longshore uniform plane beach with monochromatic, obliquely incident waves. It is found that the mismatch at the upstream cross-shore boundary tends to propagate away from the surf zone as if choosing a least-resistance path while the influence of the errors in the downstream boundary condition is limited to the adjacent area of the downstream boundary. Both the numerical and analytical solutions show that errors in the longshore current specified at the upstream boundary exponentially decay in the surf zone at a rate proportional to the bottom friction. In the case of excessive flux given at the cross-shore boundaries, a circulation cell tends to develop in the offshore region where the errors caused by the boundary mismatch increase with the cross-shore width of the model domain.