Stability of a Helmholtz Velocity Profile in a Continuously Stratified, Infinite Boussinesq Fluid—Applications to Clear Air Turbulence

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Abstract
The Kelvin–Helmholtz problem deals with the stability of fluids where both shear and stable stratification are restricted to a layer. In observed shear instability in the atmosphere, stable stratification rarely disappears outside the shear zone. In order to get some idea of the implications of this fact, I have investigated the stability properties of a particularly simple configuration: a Helmholtz velocity profile in a continuously stratified, infinite Boussinesq fluid. For a basic discontinuity 2U and Brunt-Väisälä frequency N, I find that perturbations with horizontal wavenumbers k, such that k2>N2/(2U2), are unstable and decay away from the shear zone. In addition, the shear zone is capable of supplying energy to neutral internal gravity waves, for which k2N2/(2U2), are unstable and decay away from the shear zone. In addition, the shear zone is capable of supplying energy to neutral internal gravity waves, for which k2<N2/U2, which propagate away from the shear zone. A particular wavenumber, k2 = N2/(2U2), is shown to be most efficient at carrying energy away from the shear zone. However, additional calculations suggest that for the configuration consi...

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