LINEAR AND FINITE-AMPLITUDE LOCALIZED BAROCLINIC INSTABILITY

The linear and finite-amplitude dissipative dynamics of unstable, zona lly localized baroclinic disturbances is investigated in cases where t he supercriticality varies in the zonal direction. The zonal confineme nt occurs due to O(1) variations of the frictional influence on the cu rrent's instability. A two-layer f-plane model is used. No meridional shear is present in the basic shear flow. When the basic current is eq ual and opposite in the two layers, two zonally localized modes with t he same growth rate and opposite symmetries exist for all unstable par ameter values. Thus, an infinite family of unstable modes formed from an arbitrary linear combination of these two modes exists, This degene racy persists in finite amplitude. Hence, the phase of individual cres ts in the disturbance is a function of initial conditions even for dis sipative localized instabilities. The presence of a mean barotropic fl ow reduces the growth rates of the localized disturbances and expunges the symmetry properties of the mode and the resulting degeneracy. The disturbance becomes time dependent due to phase translation of crests . Localized modes exist even when the flow in both layers is in the sa me direction. In finite amplitude there is a weak vacillation in energ y level. A discussion of the appropriate boundary condition for the lo calized modes suggests that the total geostrophic perturbation streamf unction should vanish on the flow boundaries.