Finite-amplitude wave action diagnostics based on Bjerknes circulation

The wave-mean flow interaction theory is most complete at the order of square wave amplitude, but its applicability for large-amplitude waves is limited. Here we characterize wave action (or pseudomomentum) as changes in relative circulation around potential vorticity (PV) contour following displacements on isentropic surface. For a given PV contour on isentropic surface, we first transform it into a zonal circle without changing enclosed mass and the absolute circulation around it. The relative circulation for this zonal circle defines a “basic state” flow, or Cb. The difference between the relative circulation around the original PV contour, Cr, and Cb defines the gain of circulation due to displacement of the contour and is a measure of wave action. We will use this diagnostic to quantify amplitude of Rossby waves and its propagation characteristics in the equivalent latitude-potential temperature plane.