Nonlinear saturation of baroclinic instability. Part I: The two- layer model

Abstract

For the special case of the Phillips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed εβ2/3, where ε=(U-Ucrit)/Ucrit is the (relative) supercriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ε<1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, "close' to a zonal state. -from Author