Upper-tropospheric synoptic-scale waves. Part I: maintenance as Eady normal modes

Abstract

An analytical model of waves is developed on Eady basic states that have uniform tropospheric and stratospheric potential vorticity. While the standard Eady basic state represents the limiting case of infinite stratospheric static stability, it is found that the standard Eady normal-mode characteristics hold in the presence of realistic tropopause and stratosphere. In particular, the basic states studied support upper-level normal modes of synoptic scale, which are also nonlinear solutions of the quasigeostrophic equations. It was demonstrated earlier that the upper-level modal solutions do not exist in the presence of even infinitesimal tropospheric gradients of potential vorticity. However, it is shown here that the limit of the Eady neutral mode is approached smoothly by solutions that decay even more slowly as the gradients of potential vorticity vanish. -from Authors