On baroclinic instability of curved fronts

Baroclinic instability has traditionally been examined using a model of a straight front in approximate geostrophic and hydrostatic balance. However, mesoscale curved fronts and eddies are ubiquitous in the oceans and their curvature may have an impact on baroclinic instability. In this study, we present modifications of the classical Eady and Charney problems, introducing a small amount of curvature in the small-Rossby, large-Richardson number limit. Employing quasi-geostrophic scalings for a predominantly zonal flow in cylindrical polar coordinates, we derive the governing equation of perturbation pressure in the presence of small curvature, treating this quantity as a deviation from a straight front. We find the importance of curvature principally arises through the potential vorticity (PV) gradient. Consequently, although curvature enters the Eady model via an introduction of so-called Green modes, the introduction of curvature does not modify the most unstable mode. In Charney’s model, however, the curvature of the flow introduces a depth scale that governs the vertical extent of the unstable modes and whose importance often presides over planetary beta. We find that introducing cyclonic curvature in Charney’s model increases the horizontal wavelength of the most unstable mode. We also report that curvature modifies the vertical buoyancy flux by extending the vertical scale of the most unstable mode. The possible consequences of these results are discussed. Since our present-day understanding of baroclinic instability assumes centrifugal forces in the mean state to be zero and since this undergirds existing eddy parameterizations, this study (1) offers a new interpretation of at least some of the observed vortices in the ocean and (2) suggests a weakly-curved Charney model might inform future sub-grid-scale parameterizations of baroclinic instability of curved fronts in the oceans.