Regular and Chaotic Oscillations in a Geostrophic Flow with Vertical Shear

Abstract

In the framework of a two-level quasi-geostrophic model, the stability of flow with a constant vertical shear is investigated. Analytical expressions for the increment of perturbation growth in linear stability theory were obtained. The Galerkin method with three basic Fourier harmonics was used to describe the nonlinear dynamics of perturbations. A nonlinear system of ordinary differential equations is formulated for amplitudes of Fourier harmonics. It is shown that in the absence of bottom friction all solutions of the system describe periodic mode of nonlinear oscillations or vascillations. The situation changes fundamentally in the model with bottom friction. In this case, for a wide range of parameter values, the system solutions exhibit complex chaotic behavior. Thus, chaos or turbulence emerges for large-scale motions.