A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas

Abstract

Considerable scientific and practical interest exists in ascertaining the dynamic processes in shallow seas. This is especially true for China having a vast area of shallow seas. To simulate the observed data and study the dynamical mechanism of waves and currents in shallow seas a numerical model is developed in this paper. In view of the notable nonlinearity of shallow sea waves and currents, and in order to solve the current distribution in the vertical direction, and to examine the effect of variable eddy viscosity, the model proposed is a three-dimensional nonlinear one with variable eddy viscosity. The eddy viscosity can be considered as a physically acceptable arbitrary function of depth, which is realized in terms of a Sturm-Liouville System. The currents are expressed by using the eigenfunctions satisfying the Sturm-Liouville System just mentioned. A boundary-value problem (or an initio-boundary-value problem) of free surface elevation is derived. And then, the application of the proposed shallow sea model to nonlinear tides, ultra-shallow water storm surges and steady circulation is given, respectively. Finally, a generalized linear law between the bottom friction and the transport is derived.