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Subcritical Rossby Waves in Zonal Shear Flows with Nonlinear Critical Layers
Author(s) -
Maslowe S. A.,
Clarke S. R.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01425
Subject(s) - rossby wave , physics , nonlinear system , instability , rossby number , classical mechanics , shear flow , mechanics , mathematical analysis , wavenumber , shear (geology) , dispersion (optics) , mathematics , geology , turbulence , optics , quantum mechanics , petrology , atmospheric sciences
It was shown by Benney and Bergeron [1] that singular neutral modes with nonlinear critical layers are mathematically possible in a variety of shear flows. These are usually subcritical modes; i.e., they occur at values of the flow parameters where their linear, viscous counterparts would be damped. One question raised then is how such modes might be generated. This article treats the problem of Rossby waves propagating in a mixing layer with velocity profile ū = tanh y . The beta parameter, which is a measure of the stabilizing Coriolis force, is taken to be large enough so that linear instability cannot occur. First, computed dispersion curves are presented for singular modes with nonlinear critical layers. Then, full numerical simulations are employed to illustrate how these modes can be generated by resonant interaction with conventional nonsingular Rossby waves, even when the singular mode is absent initially.