Mean Flow Evolution of a Baroclinically Unstable Potential Vorticity Front

Abstract

Quasi-linear theory and numerical models are used to study the mean flow modification of a two-layer shallow water baroclinically unstable flow as a function of Rossby number. This flow has an upper-layer potential vorticity front overlying a quiescent lower layer and is used as a simple representation of the Gulf Stream. Quantities derived from an analytical expansion in the small meander amplitude limit of the (quasi-linear) equations are found to compare quantitatively well with numerical model simulations of the flow in small amplitude and to pertain qualitatively even beyond the instability equilibration, where the meander amplitude is as large as the meander wavelength. The baroclinic evolution is similar for all Rossby numbers, with differences arising from increased asymmetry of the flow with increasing Rossby number. The equilibration of the instability is similar for all Rossby numbers and is due to the acceleration of a strong barotropic shear. This acceleration is predicted from the small amplitude analysis. Quasigeostrophic diagnostics are shown to be useful even for large Rossby number flows such as the Gulf Stream. One qualitative difference that appears is that as the mean flow is modified, a lateral separation of the zonal mean potential vorticity front and the jet maximum appears, consistent with Gulf Stream observations. This feature is found only for finite Rossby number flows.