Bounds for initial growth rates on a non-geostrophic f-plane with lateral walls

Abstract

Bounds for the growth rate in the non-geostrophic non-hydrostatic baroclinic instability problem of Eady, with or without lateral walls is considered. An application of Fourier transforms and Sturm Liouville contraction shows that the growth rate cannot exceed the largest positive root of the equation

σ⁴ + (N² - ூn²) σ² - ூn²f² = 0

where n denotes the vertical wind shear. N is the Và sà -Brunt frequency. A simple physical argument is shown to give the same result.