On the topographic dephasing and amplitude modulation of nonlinear Rossby wave interactions

Abstract

Abstract A theoretical study is presented describing large-scale topographic dephasing and amplitude modulation of Rossby wave triads. The model equations are derived via a multiple-scale asymptotic expansion in which it is assumed that topographic gradients vary over a length-scale comparable to the length-scale over which the nonlinear interactions make an order-one contribution to the dynamics. The wave-wave interactions conserve both energy and enstrophy, and preserve the Manley-Rowe relations. It is shown that, in the presence of topographic forcing, the nonlinear energy exchange will induce a permanent wavenumber mismatch in the sense that the wave resonance conditions are no longer completely satisfied. The detuning of the wave triad results in a significant reduction in the energy transfer between the individual waves. The magnitude of the wavenumber mismatch is shown to be dependent on the initial envelope amplitudes, the magnitude of the topographic slope parameter and the underlying carrier wav...