An Illustrative Model of Instabilities in Meridionally and Vertically Sheared Flows

Abstract

An analytic model is formulated to study the characteristics of shear instabilities in meridionally and vertically sheared flows. The model is based on the quasigeostrophic equations in two layers. The layers are divided into sections of piecewise uniform potential vorticity. An algebraic dispersion relation is obtained for the complex phase speed c. The magnitude and the sign of the potential vorticity jumps, their meridional separation, the barotropic shear, and the wavenumber of the modes determine the stability of the system. Solutions describe not only pure baroclinic and barotropic instabilities, but also mixtures of these instabilities. The influences of linearly sheared barotropic flows on baroclinic instability are studied in detail, with an emphasis on the direction of vertically integrated momentum flux. The model's implications for the nonlinear life cycle of baroclinic waves are also discussed.