Nonlinear aspects of symmetric instability

What is the ultimate state of a region of the atmosphere which is initially unstable to two-dimensional symmetric disturbances? The two initial states used are a region of uniform negative potential vorticity (PV), confined by two horizontal surfaces with either periodic conditions or walls at the vertical boundaries, and second, a larger domain of positive PV with an embedded zone of negative PV remote from the boundaries. The results show that the PV (and hence the instability) evolves due to boundary fluxes and internal dissipation in a way which can be simply deduced by consideration of the form of the PV generation terms. This evolution can be counterintuitive; for example, no-slip thermally conducting boundaries which imply boundary momentum and heat fluxes cannot change the volume-average PV. An important conclusion is that a parameterization of subgridscale turbulence that allows heat and momentum to flow down their mean gradients does not lead to down-gradient PV flux. The proposal is made that a parameterization of down-gradient PV flux has greater justification from a dynamical viewpoint. -from Authors