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Finite-amplitude Kelvin-Helmholtz billows

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Abstract

Periodic solutions of the nonlinear Boussinesq equations are described. It is pointed out that under typical atmospheric conditions, the critical layer phase change of linearized theory is greatly modified by nonlinear effects. New eigensolutions are obtained as a result. In particular, a continuous spectrum of neutral waves is possible when the Richardson number is greater than 1/4; such waves are not possible in the linear theory. The solutions in the critical layer have a ‘cat's-eye’ structure that is locally unstable at the edges of the cat's-eyes. The resulting picture bears a close resemblance to radar observations of clear-air waves.

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  1. Dept. of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, Mass., USA

    S. A. Maslowe

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  1. S. A. Maslowe
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Maslowe, S.A. Finite-amplitude Kelvin-Helmholtz billows. Boundary-Layer Meteorol 5, 43–52 (1973). https://doi.org/10.1007/BF02188310

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