Physical Mechanisms of Nonlinear Equilibration of a Baroclinically Unstable Jet over Topographic Slope

Spatio-temporal evolution of meanders on a baroclinically unstable jet over a topographic slope is investigated using pulse asymptotics and numerical simulations. An unperturbed jet is prescribed by a potential vorticity front in the upper layer overlaying intermediate layers with weak potential vorticity gradients and a quiescent bottom layer over a positive (same sense as isopycnal tilt) cross-stream topographic slope.An initially localized meander evolves into a wave packet growing and propagating downstream. The pulse asymptotics oflinear waves allows to characterize the structure of amplifying baroclinic wave packets by spatio-ternporal modes which grow exponentially along some rays x/t=const but decay along other rays. In a fully nonlinear numerical solution the instability growth is compensated by the nonlinear terms and the central part of wave packet saturates. The upstream and downstream development ofthe disturbance near the leading and trailing edges ofthe wave packet obeys the linear wave theory.For a weak bottom slope of0.002 the growth rate is only 10% less than that for a flat bottom. Nevertheless, meanders over a flat bottom are able to pinch offresembling warmand cold-core rings, while in the presence ofa weak bottom slope the maximum amplitudes of meanders and associated deep eddies saturate without eddy shedding.Two physical mechanisms are important to understand the effects of topographic slope: It efficiently controls the nonlinear meander growth via constraining the development ofassociated deep eddies. The bottom slope modifies the evolution ofdeep eddies and causes their phase displacement in the direction ofthe upper layer troughs /crests, thus limiting growth ofthe meanders.Behind the wave packet deep eddies form a nearly zonal circulation which stabilizes the jet. The main equilibration mechanism is homogenization ofthe lower layer potential vortic ity by deep eddies.