GROWTH AND DECAY OF FINITE-AMPLITUDE BAROCLINIC WAVES.

Abstract

The finite-amplitude dynamics of an unstable baroclinic wave in an f-plane, two-layer model is examined in the case where the degree of Ekman friction is unequal in the two layers. In particular, the case is examined where one layer is free of frictional dissipation. The method employed requires the calculations of the wave amplitude evolution on two long-time scales in order to describe the essential equilibration of the wave which at intermediate times is rendered unstable by asymmetric Ekman dissipation. The method of reconstitution is used to combine equations appropriate for each epoch of the wave's history to provide a single equation useful for calculation. The main physical result is the emergence of a finite lifetime for the unstable wave. The wave grows, equilibrates and then decays, leaving a wave-free state and an altered zonal flow with reduced potential energy. The speculation is offered that this process will be repetitive with the addition of a weak dissipative process to restore the wave-free state to its initial configuration.