The Effect of Dissipation on Spatially Growing Nonlinear Baroclinic Waves

Abstract

The question of convective (i.e., spatial) instability of baroclinic waves on an f-plane is studied in the context of the two-layer model. The viscous and inviscid marginal curves for linear convective instability are obtained. The finite-amplitude problem shows that when dissipation is O(1) it acts to stabilize the waves that are of Eady type. For very small dissipation the weakly nonlinear analysis reveals that at low frequencies, contrary to what is known to occur in the temporal problem, in addition to the baroclinic component a barotropic correction to the ?mean? flow is generated by the nonlinearities, and spatial equilibration occurs provided the ratio of shear to mean flow does not exceed some critical value. In the same limit, the slightly dissipative nonlinear dynamics reveals the presence of large spatial vacillations immediately downstream of the source, even if asymptotically (i.e., very far away from the source) the amplitudes are found to reach steady values. No case of period doubling or aperiodic behavior was found. The results obtained seem to be qualitatively independent of the form chosen to model the dissipation.