Numerical Study of Linear Stability

Abstract

This chapter deals with the method of normal modes widely used for the linear stability study of atmospheric and hydrodynamic flows on a sphere. It is the most effective and constructive technique allowing to find exponentially growing perturbations at the initial stage of the instability when the perturbation is still small and their behavior is well described by the linearized equation. However, the linear approximation ceases to function when the unstable perturbation gets big enough, and therefore the stability by linear approximation does not guarantee the nonlinear stability in the sense of Liapunov (to small but finite perturbations). Nevertheless, the instability by linear approximation means the Liapunov instability.