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On parametric instabilities of finite-amplitude internal gravity waves

Published online by Cambridge University Press:  20 April 2006

J. Klostermeyer
J. Klostermeyer
Affiliation:
Max-Planck-Institut für Aeronomie, 3411 Katlenburg-Lindau, FRG
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Abstract

The equations describing parametric instabilities of a finite-amplitude internal gravity wave in an inviscid Boussinesq fluid are studied numerically. By improving the numerical approach, discarding the concept of spurious roots and considering the whole range of directions of the Floquet vector, Mied's work is generalized to its full complexity. In the limit of large disturbance wavenumbers, the unstable disturbances propagate in the directions of the two infinite curve segments of the related resonant-interaction diagram. They can therefore be classified into two families which are characterized by special propagation directions. At high wavenumbers the maximum growth rates converge to limits which do not depend on the direction of the Floquet vector. The limits are different for both families; the disturbance waves propagating at the smaller angle to the basic gravity wave grow at the larger rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 367 - 377
Copyright
© 1982 Cambridge University Press

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