On the Three Dimensional Mass-Weighted Isentropic Time Mean Equation for Rossby Waves

Abstract

The mass-weighted isentropic zonal mean (Z-MIM) equations derived by T. Iwasaki are powerful tools for diagnosing meridional circulation and wave-mean interaction, especially for the lower boundary and unstable waves. Recently, some studies have extended the equations to three dimensions by using the time mean instead of the zonal mean. However, the relation between wave activity flux and residual mean flow (not mass-weighed mean flow) is unclear. In the present study, we derive the three-dimensional (3D) wave activity flux and residual mean flow for Rossby waves on the mass-weighted isentropic time mean equations. Next, we discuss the relation between the obtained formulae and 3D transformed Eulerian-mean (TEM) equations.