Near-Symmetric Instability for General Prandtl Number

Abstract

An analysis of the stability of a simple, baroclinic flow to perturbations whose horizontal wave vector lies in and near the vertical plane containing the density gradient has been performed. The Ekman number (E) and ?azimuthal? wavenumber (α) were both assumed ?1, and expansions about these quantities were performed for the eigenmodes and Richardson number (R). Agreement with the previous analysis of Busse and Chen that the correction to the critical R was O(α) for Prandtl number (P) away from unity was obtained. An expression for the correction to the critical R for arbitrary P, and an approximate expression for P = 1 were obtained as new results. The correction for P = 1 has the same sign as that for P < 1, and is O(αE?). This result compares well with the numerical results of Miller and Antar for small E.