Effects of cross-shore boundary condition errors in nearshore circulation modeling

The paper analyzes the effect which prescribed errors in the cross-shore boundary conditions for a computational domain along a beach have on the flow field predicted inside the domain. This problem is relevant because errors in boundary conditions are unavoidable when modeling limited domains of a nearshore region. For simplicity, we consider a longshore uniform plane beach with monochromatic, obliquely incident waves, and assume depth uniform currents. It is then studied analytically and numerically how small perturbations of the boundary conditions along both upstream and downstream cross-shore boundaries spread inside the computational domain. It is found that the errors at the upstream cross-shore boundary tend to spread over a long distance downstream of the boundary, while the influence of the errors in the downstream boundary condition is limited to the adjacent upstream area of the computational domain. Both the numerical and analytical solutions show that the errors introduced at the upstream boundary decay exponentially in the surf zone at a rate proportional to the bottom friction. A simple formula is developed to estimate the influence distance of the upstream errors. If we consider the mismatch in the volume flux at the upstream boundary, the error merely redistributes in the cross-shore direction to conserve volume. In the case of excessive flux or velocity specified at the cross-shore boundaries, a circulation cell tends to appear in the offshore region where the errors caused by the boundary mismatch increase with the cross-shore width of the model domain.