Barotropic and inertial instabilities in the hurricane outflow layer

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Abstract
The shallow water, linear model in cylindrical coordinates is used to investigate barotropic and inertial instabilities in the tropical cyclone outflow layer. When the mean state wind satisfies the condition |ζ|«|f 0 the instabilities found in our model are equivalent to the barotropic instabilities calculated with the quasi-geostrophic potential vorticity equation. The maximum instability is internal and appears at azimuthal wavenumber one. When an observed (composite) hurricane outflow layer is assumed as a basic state, the largest barotropic growth rate (e-folding time scale ≈7 days) appears at azimuthal wavenumber s = 1 and equivalent depth about 30 m. The maximum growth for s = 2 is about four times smaller than for s = 1 and occurs with the external mode. Inertial instability dominates at the very small equivalent depths and is likely to be stabilized by friction.

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