Local and Global Baroclinic Instability of Zonally Varying Flow

Abstract

The baroclinic instability characteristics of zonally inhomogeneous basic states are examined with the intent of clarifying the factors governing the regional distribution of cyclogenesis. The vertical shear of the basic state wind is allowed to vary gradually in the zonal direction, so as to permit the representation of zonally localized regions of high baroclinicity. The resulting eigenvalue problem is solved directly by numerical means and also analytically via a WKB analysis. It was established that flows with localized baroclinicity can support two distinct classes of unstable modes, which we call “local” and “global.” The local modes have peak amplitude downstream of the point of maximum baroclinicity, decay to zero exponentially upstream and downstream of the peak and do not require zonally periodic boundary conditions for their existence. The growth rate of a local mode is equal to the absolute growth rate (in the sense of Merkine) determined locally at the point of maximum shear. The absolute growth rate decreases when the vertically averaged zonal wind is increased, in contrast with the conventional locally determined maximum growth rate. Further properties of the local modes are discussed. The global modes, on the other hand, require periodic boundary conditions for their existence and have growth rates which are sensitive to the average baroclinicity over the domain. Global modes take a much longer time than local modes to emerge from random initial conditions. On the basis of these results, it is suggested that the locally determined absolute growth rate is a useful diagnostic for assessing the stability of inhomogeneous flow. In this connection, a tentative analysis of the results of Frederiksen on planetary wave instabilities was found to be encouraging. Although only a simple model of baroclinic instability was considered in the present work, the techniques developed can be generalized to any kind of instability provided that there is a separation in spatial scale between the eddies and the basic state. It is thus proposed that there is a general link between absolute instability and the instability of nonparallel flow.