On the Development of a Rossby Wave Critical Level

Abstract

The asymptotics of the analysis of Dickinson (1970) on the development of a Rossby wave critical level are reexamined. These linear results are used to discuss certain aspects of the development of the nonlinear critical level for Rossby waves. In particular it is shown that the critical layer becomes fully nonlinear in a (nondimensional) time scale of O(e-??), where e is a parameter measuring the amplitude of the forced wave, and that all harmonies are likely to be important in the critical layer after this time.