A Numerical Investigation of Hydrodynamic Instability and Energy Conversions in the Quasi-Geostrophic Atmosphere. Part II

Abstract

The numerical model of Part I is used in certain experiments designed to reveal special instability effects caused by the vertical walls which specify the lateral boundary conditions at the northern and southern boundaries of the atmosphere. In these examples the walls suppress instability of the barotropically dominated perturbations and have little influence on the westward progressions of the unstable waves. Small-scale eddy momentum and heat diffusion processes are simulated in an example of a basic westerly wind field containing absolute vorticity extrema. The inclusion of these mechanisms is found to inhibit instabilities of all zonal wavelengths, with major effects noted for short shallow waves. The significant modifying influence is attributed to large effects of drag at the ground. The behavior of an unstable wave interacting with the zonal current is obtained through nonlinear numerical calculations. The equilibrium state approached in the presence of a time-independent diabatic heating differential oscillates about a steady state. The several energy conversion rates vary in time in such a way as to minimize the time-rates-of-change of the different types of energies. The equilibrium energy levels appear to be governed by the required baroclinic process, and the resulting period of the oscillating regime is dictated by the barotropic mechanism.