Upper-Tropospheric Synoptic-Scale Waves. Part I: Maintenance as Eady Normal Modes

Abstract

Upper-tropospheric waves are important in midlatitude synoptic-scale dynamics. Their life duration is typically longer than time scales for disruption by the ambient shaer and they often induce surface cyclogenesis. In this paper a dynamical model is proposed for the maintenance of these upper-level waves based on the upper-level Eady normal modes. An analytical model of waves is developed on Eady basic states that have uniform tropospheric and stratospheric potential vorlicity. 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.