Baroclinic instability of semi‐geostrophic fronts with uniform potential vorticity. I: An analytic solution

摘要

AbstractBaroclinic instability of uniform potential‐vorticity flow between solid upper and lower boundaries is analysed. The instability is driven by meridional temperature gradients on the boundaries. The classic Eady model of baroclinic instability uses just this system with the further idealization that the temperature gradients in the basic state are uniform. Here, this last idealization will be replaced with a complementary one in which the basic‐state temperature gradients are taken to be concentrated in a front. The analysis then takes advantage of the fact that the boundary temperature anomalies created by the growing baroclinic wave are localized at the front. The dependence of the growth rates and phase structure on wave number are remarkably similar to those of the Eady model. The wave number of maximum instability and the short‐wave cut‐off differ from those of the Eady model by less than 2 and 10 respectively. The solution is asymptotic in the limit of zero frontal width in geostrophic coordinates. For a physical flow this limit can never be achieved, but comparison with direct numerical solutions shows that the analytic solution is still accurate at physically relevant frontal widths. Part I develops the solution based on an equation for the evolution of the displacement of the surface and upper fronts. Part II will look at the three‐dimensional structure of the disturbance in mo