On group velocity and energy flux in planetary wave motions

In planetary waves on a β-plane, the energy flux vector up(calculated from the velocity uand pressure p) is generally different in both magnitude and direction from the flux vector Ecg(calculated from the energy density Eand group velocity cg). This apparent discrepancy is shown to be due to a certain arbitrariness in the definition of energy flux. The two vectors just defined are found to differ by a non-divergent vector (ϖA/ϖy, − ϖA/ϖx) where A = 14p f aa∗and ϱ, f, adenote the density, coriolis parameter and local wave amplitude respectively.