Nonlinear Baroclinic Equilibration in the Presence of Ekman Friction

Abstract

wo theories for the nonlinear equilibration of baroclinic waves in a two-layer fluid in a ? channel are tested by comparison with high-resolution numerical simulations. Predictions are tested for a range of parameters (?, ?), where the inverse criticality ? measures the degree of instability and the quasigeostrophic Ekman number ? measures the strength of Ekman friction. The first theory, from Warn, Gauthier, and Pedlosky (WGP), is formally valid for marginally unstable waves at ? = 0. The second, from Romea, is formally valid for nonzero ? and for waves that are marginally stable with respect to a different criterion, which enters because of the dissipative destabilization of otherwise stable waves by Ekman friction. The predictions of the two theories are in conflict in the limit ? ? 0. When ? is slightly greater than zero, it is found that the WGP accurately predicts the maximum wave amplitude attained during a baroclinic life cycle across a significant range of parameter space. By contrast, accurate predictions of the long-time asymptotic wave amplitude are obtained only from Romea?s theory, even for those cases where WGP describes the initial behavior during the life cycle accurately. The results first indicate the importance of understanding the nonlinear equilibration mechanism of dissipatively destabilized waves. Second, it follows that baroclinic adjustment theories formulated from inviscid and frictionless stability criterion make demonstrably incorrect predictions for the equilibrated state, even in the limit of vanishing Ekman friction.