Some Comparisons of Atmospheric Internal and Boundary Baroclinic Instability

Abstract

The existence of boundary baroclinic instability (as exemplified by the Eady or Charney problems) and internal baroclinic instability, which requires the potential vorticity gradient to take both signs in the fluid interior, is unified by regarding the boundary temperature gradients in the external problem as equivalent to infinitely thin sheets of nonzero potential vorticity gradient. It is shown that this analogy can be generalized from the quasi-geostrophic to the primitive equation systems. The linear instability problem on the sphere is examined using the primitive equations; the results are consistent with those of simple conceptual models where potential vorticity gradients are concentrated in thin sheets. The normal modes are integrated into the nonlinear regime, and it is shown that the low-level potential vorticity gradients evolve in a similar way to the surface temperature fields in the lifecycles of external modes. Frontal structures are absent, though the enstrophy cascade produces narrow, elongated low-level features around the time of maximum wave activity, Finally, a lifecycle for a boundary unstable flow is compared with that for an initial flow, which is identical except that the surface potential vorticity sheet is thickened to form a finite layer of negative potential vorticity gradient. The evolution of the two cases is remarkably similar except for frontogenesis in the external case.