Scale Selection of Baroclinic Instability—Effects of Stratification and Nongeostrophy

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Abstract
A simple two-dimensional linear stability analysis is presented to study the characteristics of the scale selection and structure of baroclinic cyclogenesis. Effects of a realistic vertical thermal structure of the environment and the related nongeostrophic wind are investigated in detail. Both short (mesoscale) waves trapped in the lower layer with a small static stability and long waves extending throughout the column are unstable, which supports Blumen's results. The integral constraints imply that the vertical structure of the stratification can provide an “internal lid” to confine the wave into the mixed layer. Nongeostrophic effects become important as Richardson number decreases as pointed out by Stone; the scale of the most unstable Eady's mode becomes sensitive to the change of shear, unlike the geostrophic case. The measure of the horizontal scale of the disturbance is the modified Rossby radius of deformationwhere Λ is the vertical shear and provides O(Ri−½) correction to the conventional definition. However this shear dependence is drastically different between the full nongeostrophic system and the one with geostrophic momentum approximation. Another nongeostrophic mode—the weakly unstable, small-scale waves found by Stone—is identified as an instability due to the inertia critical layer which is sustained by the resonance between one of the boundary modes and inertia–gravity modes. It is analytically shown that this mode may exist even without one of the boundaries, unlike Eady's mode. The growth rates and the shallow structure of the most unstable short Eady waves are generally in agreement with observed early stages of winter storms (coastal cyclogenesis, polar lows, and comma clouds), though some observed cases have a considerably deep structure.

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