A Numerical Model of Convection Driven by a Surface Stress and Non-Uniform Horizontal Heating

Abstract

Abstract This paper examines the two-dimensional convective motion of a nonrotating incompressible Boussinesq fluid heated non-uniformly from below. The fluid container is rectangular; the side and top boundaries are insulating and rigid. A linear temperature field is maintained along the bottom boundary. Using the DuFort-Frankel scheme for diffusion and the Arakawa scheme for advection, the governing vorticity and temperature equations are integrated numerically for two cases, the first having a stress-free bottom boundary and the second having a constant stress along the bottom boundary. In the first case, a single convective cell develops; an intense buoyant jet of fluid rises from the warmer section of the bottom while there is a more uniform sinking motion over the cooler section of the bottom. The cell asymmetry, the circulation, and the convective heat transfer increase markedly with increasing Rayleigh number (based here on fluid properties, cell height, and the horizontal temperature difference a...