The circle diagram in the group velocity domain for Rossby wave under the horizontally non-uniform flow

Abstract

Rossby wave propagation theory is reviewed under two kinds of non-uniform basic flows: the zonal mean (ZM) and horizontally non-uniform (HN) flows in this study. The diagrams in the wavenumber domain for stationary and non-stationary waves embedded in the ZM flow are given and discussed in comparison with previous studies. Then a circle diagram in the group velocity domain for waves embedded in the HN flow is derived from the formulas in forms of three vectors: the wavenumber, background wind and gradient of basic-state absolute velocity. Given the basic state, we can identify the maximum and minimum magnitude of group velocity and its departure from the background wind. These results provide insights into Rossby wave propagation behaviors in the real atmosphere.