Diabatic Potential Vorticity Over the Global Tropics

Abstract

Most readers are familiar with the basic concepts of conservation of absolute vorticity and potential vorticity. The conservation of absolute vorticity is generally used in a two-dimensional context, where the effects of heat sources and sinks, divergence, vertical motion and friction are ignored and the vertical component of the vorticity, i.e., $\nabla \times \mathbf{V}+f$ is conserved following a parcel. The conservation of potential vorticity, on the other hand, is properly applied to three-dimensional motions of parcels on isentropic surfaces, following the seminal work of Ertel. Here again the heat sources and sinks and the friction terms are ignored. The effects of divergence and vertical motion, however, are retained. In a very simplistic sense, we can use the following two approximate equations:

$$ \frac{{d{\zeta_a}}}{dt }=-{\zeta_a}\nabla \cdot \mathbf{V} $$

$$ \frac{{d{\varGamma_d}}}{dt }={\varGamma_d}\nabla \cdot \mathbf{V} $$