The Nonlinear Evolution of Idealized, Unforced, Conditional Symmetric Instability: A Numerical Study

Abstract

A two-dimensional version of the Penn State?NCAR mesoscale model (MM4) has been used to simulate the life cycle of conditional symmetric instability (CSI) under conditions of no deformational or planetary boundary layer forcing with the model starting from idealized initial conditions. Detailed diagnostics from the growth, decay, and post-CSI stages of the life cycle are presented, and some of these features are compared to expectations from linear theory. The life cycle features include local areas of potential and inertial instability and specific patterns of ageo-strophic zonal flow. Local areas of increased and decreased dry potential vorticity (q), including areas of negative q, develop from the initially everywhere-positive q field, principally because of the horizontally differential diabatic heating. Negative wet-bulb potential vorticity (qw) is principally advected into the upper troposphere by the CSI updraft, though some changes in qw do occur because of the diffusion of temperature. Model-output soundings along surfaces of constant absolute momentum (m) show that lower-tropospheric thermodynamic stabilization and a decrease in slantwise convective available potential energy occur during the simulation. Net changes produced by the CSI circulations include low-level frontogenesis, upper-level frontolysis, and local buoyant and inertial stabilization-destabilization. The modeled updraft slope is between that of the surfaces of constant wet-bulb potential temperature (?w) and that of the surfaces of constant m, since the viscosity and finite grid spacing yield an unstable mode with a finite updraft width. Such a mode differs from the inviscid mode, which has an infinitely narrow updraft width and a slope along the ?w surfaces. The cessation of the CSI is not due to the removal of the area of negative moist potential vorticity. Instead, linear stability analysis suggests that the cessation is due to the stabilization of modes with resolvable updraft widths and, possibly, to the depletion of the water vapor supply. Idealized studies such as these do not attempt to achieve absolute realism but are necessary steps in the methodical process of linking simple theoretical treatment of CSI with the complex observations; they may be useful as aids in interpreting observational data or numerical model simulations of real-atmosphere cases.