On the Thickness Ratio in the Quasigeostrophic Two-Layer Model of Baroclinic Instability

Abstract

t is shown that the classical quasigeostrophic two-layer model of baroclinic instability possesses an optimal ratio of layer thicknesses that maximizes the growth rate, given the basic-state shear (thermal wind), beta, and the mean Rossby radius. This ratio is interpreted as the vertical structure of the most unstable mode. For positive shear and beta, the optimal thickness of the lower layer approaches the midheight of the model in the limit of strong criticality (shear/beta) but it is proportional to criticality in the opposite limit. For a set of parameters typical of the earth?s midlatitudes, the growth rate maximizes at a lower-layer thickness substantially less than the midheight and at a correspondingly larger zonal wavenumber.It is demonstrated that a turbulent baroclinic jet whose statistical steady state is marginally critical when run with equal layer thicknesses can remain highly supercritical when run with a nearly optimal thickness ratio.