Application of a sigma coordinate sea model to the calculation of wind-induced currents

Abstract

A three-dimensional numerical sea model is formulated in terms of sigma coordinates in the vertical. The vertical grid spacing in the model is arbitrary and can be refined to give enhanced resolution in high shear regions (e.g., close to the sea surface in wind-driven flows, and/or across the thermocline in stratified flows). A method of accurately determining surface currents and indicating how fine a grid is required in the surface layer is described. The problem of determining a suitable formulation of vertical eddy viscosity to use in a model of wind-induced flow in a tidal sea is considered in detail. A formulation in which surface eddy viscosity depends upon the roughness of the sea surface and the transfer of momentum to depth by surface waves appears reasonable. Below the surface layer turbulence is related to the current at depth. Idealized calculations are performed to demonstrate the accuracy and stability of the sigma coordinate model. Results of these calculations indicate that the formulation of eddy viscosity developed in this paper can explain the high surface shears reported in lake measurements of wind-induced surface currents, and the lack of shear under strong wind conditions in the open sea ( GORDON, 1982, Journal of Geophysical Research, 87, 1939–1951 ). Surface current to surface wind ratio are also computed.