Feasability of Finite Element Methods for Oceanic General Circulation Modelling

Abstract

The response of the ocean to the action of a wind-stress at the surface has been investigated by many scientists since the middle of this century. The pioneering investigations were carried by Sverdrup (1947), Stommel (1948) and Munk (1950): they approximate the real ocean flow induced by the wind at the mid-latitudes in terms of total mass transport of a homogeneous layer of fluid of uniform depth on a beta plane (a projection of the sphere on a tangent plane where the Coriolis parameter is taken to be fo + βy, with fo and β constant, and y the north south coordinate). The fluid is set in motion by a torque which models the effects of the zonally averaged large scale wind pattern of the westerlies and the trades. Thus, the circulation appears as a gyre in which the Coriolis forces balance the pressure gradients and the driving force of the wind stress, in the greater part of the basin (Sverdrup balance); every streamline is going through a boundary layer region, in the western part of the basin, where an important dissipation of vorticity arises: this sink of vorticity is produced by bottom friction in Stommel’s model, and by lateral diffusion of momentum in Munk’s model; some non linear analytical models were then developped to include the inertial effects which are of evidence very important: Munk, Groves and Carrier (1950), Carrier and Robinson (1962), Moore (1963), Il’in and Kamenkovich (1963), Niiler (1966); but these models were questionable on many points: for example they assumed a priori the existence of steady state solutions, without proof. Thus numerical models have been developped to investigate the general time dependent non linear case: Bryan (1963) extended in the non linear and time dependent domain the Munk’s model, Veronis (1966) did the same for the Stommel’s model, Brandford (1971) realized a synthesis of the two. Since these early works, numerous contributions by numerical modellers improved our understanding of the wind induced circulation of the ocean which is impossible to review in this introduction. But, within this paper, it must be pointed out that all these numerical models have been developped on the basis of finite difference technics.