Nonlinear stability criteria for the motion of three-dimensional quasigeostrophic flow on a beta -plane

Abstract

The authors study the nonlinear stability of three-dimensional quasigeostrophic motion on a beta -plane. The criteria obtained are applicable to perturbations of both initial data and parameters in models. For verifying criteria parallel to Arnold's second theorem given by other authors, one has to calculate the lowest eigenvalue of a three-dimensional elliptic partial differential equation with variable coefficients and, for the given criteria, one needs only do the same for the two-dimensional Laplacian.