A Numerical Method for Finding Form-preserving Free Solutions of the Barotropic Vorticity Equation on a Sphere

Abstract

A numerical method is presented that allows one to obtain steady or zonally moving (i.e., form-preserving) solutions of the barotropic vorticity equation on a sphere. The solutions are characterized by nonlinear functional relationships between the streakfunction (the streamfunction in a steady or zonally moving frame of reference) and the absolute vorticity. Three new examples of steady solutions are obtained that resemble atmospheric blocking. The examples have approximately the same global structure but differ in the degree of uniformity of the streamfunction and the absolute vorticity in the blocking region. From a numerical linear stability analysis it is concluded that the example in which the absolute vorticity in this region is the most uniform is to be preferred as a description of atmospheric blocking. This conclusion is consistent with recent observational evidence.