Barotropic instability due to Kelvin wave-Rossby wave coupling

The stability of a vertically bounded, piecewise linear shear profile in a channel is analyzed using both a quasigeostrophic (QG) and primitive equati on (PE) model. The choice of a finite depth domain thus allows us to consid er more realistic flows in which the jet is vertically bounded. A potential vorticity discontinuity in the QG model can give rise to an isolated shear -generated Rossby mode that remains stable in the absence of other mean flo w discontinuities. The finite depth assumption in the QG model is of little consequence as the vertical scale of the basic state enters the dynamical equations in a trivial manner. Solving this problem in the PE model, on the other hand, leads to unstable modes not present in the QG limit. Using sem igeostrophic (SG) dynamics the authors are able to identify two modes of in stability. One occurs as a result of a Kelvin wave-Kelvin wave coupling and the other is a product of Kelvin wave-Rossby wave coupling. It is also fou nd that resonance between the Rossby mode and an unphysical "mirage wave" t akes place in SG theory, causing a spurious instability not present in the PE case in regions of parameter space where the depth of the domain tends t o infinity.