A numerical study of wind-induced motions in shallow coastal seas: model and basic experiments

Abstract

A three-dimensional linear hydrodynamical numerical model of wind-induced motions in a homogeneous, shallow sea has been developed. The model is based upon the spectral, eigenfunction approach originated by N.S. Heaps. It accomodates arbitrary variation of vertical eddy viscosity by phase- amplitude transformation of eigenfunctions and numerical solution of the vertical, eigenvalue problem. The horizontal problem is solved using a forward-time, staggered-space finite difference scheme. Comparisons to analytical solutions show that the applied method yields, after a finite inverse transformation, meaningful results of satisfactory accuracy. After verification, the model was used to stimulate several cases of vertically variable eddy viscosity grouped around four scenarios: constant eddy viscosity, eddy viscosity decreasing throughout the water column, eddy viscosity influenced by the surface and bottom boundary layers, and eddy viscosity derived from observational data. The most pronounced differences due to vertically variable eddy viscosity have been observed within the third scenario. Tentative comparison to appropriately processed current data from the Northern Adriatic has shown that vertically variable eddy viscosity can contribute to a more successful match of model predictions and empirical data.