Evolution of baroclinic wave packets in a flow with continuous shear and stratification

Abstract

Evolution equations are developed for weakly nonlinear baroclinic wave packets in a flow with continuous shear and stratification. When wave dispersion is forced by using sloping upper and lower boundaries it is shown that, for boundary slope equal to isothermal slope in the basic state, these evolution equations are transformable to the sine-Gordon equation. The relation between behaviour in this model and that in the discretelayer models of baroclinic instability is discussed, and finally solutions of the sine-Gordon equation appropriate to a periodic domain are presented and compared with experimental results.