Generalized Stability of Nongeostrophic Baroclinic Shear Flow. Part II: Intermediate Richardson Number Regime

Abstract

Abstract This work continues the generalized stability theory (GST) analysis of baroclinic shear flow in the primitive equations (PE), focusing on the regime in which the mean baroclinic shear and the stratification are of the same order. The Eady model basic state is used and solutions obtained using the PE are compared to quasigeostrophic (QG) solutions. Similar optimal growth is obtained in the PE and QG frameworks for eddies with horizontal scale equal to or larger than the Rossby radius, although PE growth rates always exceed QG growth rates. The primary energy growth mechanism is the conventional baroclinic conversion of mean available potential energy to perturbation energy mediated by the eddy meridional heat flux. However, for eddies substantially smaller than the Rossby radius, optimal growth rates in the PE greatly exceed those found in the QG. This enhanced growth rate in the PE is dominated by conversion of mean kinetic energy to perturbation kinetic energy mediated by the vertical component of zonal eddy momentum flux. This growth mechanism is filtered in QG. In the intermediate Richardson number regime mixed Rossby–gravity modes are nonorthogonal in energy, and these participate in the process of energy transfer from the barotropic source in the mean shear to predominantly baroclinic waves during the transient growth process. The response of shear flow in the intermediate Richardson number regime to spatially and temporally uncorrelated stochastic forcing is also investigated. It is found that a comparable amount of shear turbulent variance is maintained in the rotational and mixed Rossby–gravity modes by such unbiased forcing suggesting that any observed dominance of rotational mode energy arises from restrictions on the effective forcing and damping.