Instability of the Kolmogorov Flow in a Model Taking Into Account Ekman Friction and the Beta Effect

The paper studies the stability of spatially periodic flow in a model taking into account bottom friction and the beta effect. Within the framework of the linear approximation, a stability criterion for the flow in a quasi-geostrophic model with bottom friction is obtained. To describe the nonlinear stability, the Galerkin method with three basic Fourier harmonics is used. It is shown that the exponential growth of linear disturbances at the nonlinear stage of development is replaced by the regime of establishing stationary periodic disturbances. A linear model of periodic flow stability with joint consideration of bottom friction and the beta effect is developed. It is shown that taking into account the beta effect leads to the development of oscillatory instability.