Generalized Stability of Nongeostrophic Baroclinic Shear Flow. Part I: Large Richardson Number Regime

Abstract

A generalized stability theory (GST) analysis of baroclinic shear flow is performed using primitive equations (PEs), and typical synoptic-scale midlatitudinal values of vertical shear and stratification. GST is a comprehensive linear stability theory that subsumes modal stability theory and extends it to account for nonmodal interactions such as may occur among the approximately geostrophically balanced modes and the nearly divergent gravity wave modes supported by the PE. Unbounded constant shear flow and the Eady model are taken as examples and energy is used as the reference norm. Comparison is made with results obtained using quasigeostrophic (QG) analysis. While the PE and the QG dynamics give similar results for timescales of a few days, the PE initial growth rate during the first few hours exceeds the QG growth at all wavelengths and can attain values as much as two orders of magnitude greater as the wavelength decreases. This PE growth is due both to the direct kinetic energy growth mechanism, which is filtered out by QG, and to the interaction between the QG modes and the gravity waves. An important application of GST is to study shear turbulence using a method of analysis based on stochastically forcing the mean state. The PE response of the Eady model to spatially and temporally uncorrelated forcing reveals the rotational and the divergent modes support a comparable amount of variance. The observed spectrum and physical mechanisms influencing the spectrum are discussed.