Nonlinear geostrophic adjustment, cyclone/anticyclone asymmetry, and potential vorticity rearrangement

Nonlinear geostrophic adjustment, cycloneÕanticyclone asymmetry, and potential vorticity rearrangement

Within the context of the rotating shallow water equations, it is shown how initially unbalanced states possessing certain symmetries dynamically evolve to lose those symmetries during nonlinear geostrophic adjustment. Using conservation law methods, it is demonstrated that the adjustment of equal and opposite ~circular! mass imbalances results in a balanced end state where cyclones are stronge...

Precipitating Quasi-Geostrophic Equations and Potential Vorticity

Precipitating versions of the quasi-geostrophic (QG) equations are derived systematically, starting from the equations of a cloud-resolving model. The presence of phase changes of water from vapor to liquid and vice versa leads to important differences from the dry QG case. The precipitating QG (PQG) equations, in their simplest form, have two variables to describe the full system: a potential ...

Available potential vorticity and wave-averaged quasi-geostrophic flow

We derive a wave-averaged potential vorticity equation describing the evolution of strongly stratified, rapidly rotating quasi-geostrophic (QG) flow in a field of inertia-gravity internal waves. The derivation relies on a multiple-time-scale asymptotic expansion of the Eulerian Boussinesq equations. Our result confirms and extends the theory of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998,...

Nonlinear Balance and Potential Vorticity Thinking at Large Rossby Number

A note on the derivation of the quasi-geostrophic potential vorticity equation

The derivation of the quasi-geostrophic potential vorticity equation of mathematical meteorology is usually done using fairly sophisticated techniques of perturbation theory, but stops short of deriving self-consistently the stratification parameter of the mean atmospheric state. In this note we suggest how this should be done within the confines of the theory, and as a consequence we raise the...