The exact solution of the Rossby adjustment problem

Abstract

The exact solution of the Rossby (1938) adjustment problem is obtained. If a is the half-width of the initial current and λ is the radius of deformation, it is shown that Rossby's solution is asymptotically valid for a/λ <1. We examine the asymptotic solution for a/λ >1. The exact energetic relations are obtained. The numerical examples of Rossby are recalculated with the exact solution.