Stationary Response of Barotropic Weakly Nonlinear Rossby Waves to Quasi-Resonant Orographic Forcing

Abstract

Stationary solutions and their stability properties of nondissipative barctropic flow in a narrow, longitudinally periodic channel on a βplane with a sheared basic current and bottom topography are investigated. An analytical treatment is applied which has been used in studies of solitary Rossby waves and is allowed by the choice of geometry. This leads to an ordinary nonlinear differential equation for the longitude-dependent part of the solution. The equation which is obtained in the present case is formally that of an anharmonic oscillator with external forcing and weakly variable natural frequency. Approximate analytical and numerical solutions are obtained under quasi-resonant conditions. Three possible states are found in a certain range of the parameters. Of these, only two are found to be stable. The implications of the existence of multiple solutions, also found by other authors in various contexts, for the large-scale atmospheric circulation and the phenomenon of blocking are discussed.