On the generalized eigenvalue problem of Rossby waves vertical velocity under the condition of zonal mean flow and topography

Abstract

Tailleux (2003, 2012) proposed the influence of background mean flow and topography on the propagation of Rossby waves through a generalized eigenvalue problem, but the mean flow in his paper did not take latitude into account and was not ideal enough. In the middle and high latitudes, the latitude secondary shear flow (ūyy) is close to the β scale, which cannot be ignored in barotropic instability. It is an important factor affecting the propagation of Rossby waves. In this paper, the effects of mean flow and topography on Rossby wave propagation in the barotropic atmosphere are studied based on the quasi-geostrophic vortex equation. To make the physical process more involved in line with the actual atmospheric conditions, we consider both vertical and zonal mean flows. Under the semi geostrophic concept, we obtain the eigenvalue problem of vertical velocity. In the atmosphere, the dispersion relation generally has symmetry for a certain latitude. We study the northern hemisphere, so we only consider the case of negative wavenumber. By comparing the stability of Rossby waves without zonal mean current and with zonal mean current, it is found that zonal mean current has a non-ignored effect on the stability of Rossby waves, it speeds up the phase velocity, with the increase of wavenumber, the frequency decreases.