“A primitive model for the thermally and stress driven flow”

Abstract

We describe the flow driven by thermodynamic and stress forces at the upper wall of 2D and 3D rectangular basins with high aspect ratio. The mathematical model is a primitive equation with the Boussinesq approximation, since the horizontal scale is much larger than the vertical one. For the 3D basin we consider that under the condition of high aspect ratio we can assume the hydrostatic approximation in addition, which provides a fundamental equation connecting the pressure and density. Models of this type are an abstraction of large scale ocean flow.

We develop a velocity-pressure algorithm with a pressure Neumann condition in primitive variables, using a Boussinesq approximation and fixed Prandtl number. The pressure-field is updated in a one-step weighted form. We report on simulations made for several Rayleigh numbers.