A Simple Example of Galilean Invariance in the Omega Equation

Abstract

This paper is pedagogically motivated to qualitatively demonstrate basic concepts related to Galilean invariance and partial cancellation in the individual forcing terms in the traditional form of the omega equation. The analysis provides examples of the vertical distribution of the primary quasigeostrophic (QG) forcing, showing how the individual forcing terms vary in different coordinate systems while their sum remains constant. The QG forcing is described analytically using an unstable Eady wave solution, which allows depictions of QG forcing similar to those in basic atmospheric dynamics texts. The perturbation streamfunction, temperature, and vertical velocity are seen to be invariant under change of horizontal coordinate system, while the individual magnitudes of the QG vertical motion forcing are not. The total QG forcing remains invariant in all cases and is equal to the QG forcing found from the divergence of the Q vector. The figures provided can supplement those used for traditional study and may be useful to provoke classroom discussion of related QG concepts.