Nonlinear saturation of topographically forced Rossby waves in a barotropic model

A quasigeostrophic barotropic model is used to examine the nonlinear satura tion of forced Rossby waves and the role of wave-wave interactions in limit ing the wave growth. A simple mechanism, based on wave interference, is use d 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 con servation, is formulated and its domain of validity is examined with a nume rical nonlinear model. The nonlinear flow evolution is shown to bear strong similarity to the analytical quasi-linear solution and wave-mean flow inte ractions are found to be always sufficient to limit wave growth. The satura tion of the forced disturbances is shown to come through the deceleration o f 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 implica tions of this result for the observationally more relevant case of vertical ly propagating Rossby waves, explicit calculations are clearly called for.