Nonlinear Saturation of Topographically Forced Rossby Waves in a Barotropic Model

Abstract

A quasigeostrophic barotropic model is used to examine the nonlinear saturation of forced Rossby waves and the role of wave‐wave interactions in limiting the wave growth. A simple mechanism, based on wave interference, is used to produce strong transient eddy growth and an analytical linear solution for the flow evolution is used as a starting point. Given the rigid upper bound on wave growth, set by the potential enstrophy conservation principle, the linear solution is bound to break down at high forcing amplitudes. An analytical quasi-linear solution, which guarantees potential enstrophy conservation, is formulated and its domain of validity is examined with a numerical nonlinear model. The nonlinear flow evolution is shown to bear strong similarity to the analytical quasi-linear solution and wave‐mean flow interactions are found to be always sufficient to limit wave growth. The saturation of the forced disturbances is shown to come through the deceleration of the mean flow and the modification of the topographic vorticity forcing. Overall, wave‐wave interactions prove not to be important in the saturation process in the examples considered. While the authors consider the implications of this result for the observationally more relevant case of vertically propagating Rossby waves, explicit calculations are clearly called for.