Nonlinear Aspects of Symmetric Instability

Abstract

This paper addresses the question: What is the ultimate state of a region of the atmosphere which is initially unstable to two-dimensional symmetric disturbances? Such regions are believed to account for frontal rainbands and influence convection in baroclinic zones. Observations show that often the atmosphere is close to moist isentropic along absolute momentum surfaces and this state, it has been proposed, arises as a result of symmetric instability. Here we attempt to establish a set of dynamical archetypes to understand whether and how such a neutral state is established. Certain simplifying assumptions are made such as constant eddy viscosity, unsaturated flow, and simple boundary conditions to clarify the discussion. 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 entirely confined region is clearly a poor model of the atmosphere, except for atmospheric regions which are forced by the larger scale flow to remain unstable, but highlights some important dynamical aspects of the instability. Particular attention is given to the evolution of the PV field as this determines the linear growth of the instability. The results of the numerical simulations 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. Other key features include an up-scale energy transfer which promotes the largest circulation possible in the domain, frontogenesis, and the development of regions of convective and inertia] instability. The energetics suggest that the vertical heat flux is often negative leading to the conclusion that the term ?slantwise convection? may be inappropriate for this dry analogue of conditional symmetric instability. 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 abandoning down-gradient momentum flux in favor of down-gradient PV flux has greater justification from a dynamical viewpoint.