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John Marshall and Damon W. K. So

Abstract

Equilibration of planetary waves toward free-mode forms, steady solutions of the unforced, undamped equations of motion, is studied in a three-level quasi-geostrophic model on the hemisphere. A thermal mechanism is invoked, parameterized as a Newtonian process Q = −γ(TT*), relaxing the atmosphere toward a radiative-convective equilibrium temperature T* on γ −1 time scales. If T* is chosen to project onto the class of finite-amplitude stationary Rossby waves, T can closely approach T* if, simultaneously, the surface winds vanish switching off the Ekman layers at the surface. The equilibrated state is characterized by vertical phase lines, zero surface winds, vanishing diabatic heating rates and a temperature field that is phase-locked with T* corresponding to ridges over the oceans and troughs over the land. The form of the equilibrated planetary wave is contrasted with the classical thermally forced response obtained when T* does not have free-mode form. Anomaly fields calculated from the model, the difference between equilibrated and nonequilibrated waves, have a characteristic pattern which is reminiscent of Rossby wave trains.

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