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Algebraic disturbances in stratified shear flows

Published online by Cambridge University Press:  19 April 2006

G. Chimonas
G. Chimonas
Affiliation:
Cooperative Institute for Research in Environmental Sciences, University of Colorado/NOAA, Boulder
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Abstract

Algebraic disturbances, a non-modal component of the linear perturbation fields, are shown to be an essential feature of stratified shear flows. We find that they must be included even in situations where the modes form a complete set, for such completeness does not extend to the space of these ill-behaved functions.

If the Richardson number Ri is less than ¼ anywhere in the flow, the algebraic disturbances are very generally instabilities of the system, growing without limit as time t → ∞.

Both of these results are in direct contradiction with the currently accepted viewpoint. We examine the previous research in this field to locate the source of this discrepancy.

The algebraic instabilities are not form preserving, and display extreme distortion as they evolve. In the asymptotic limit they appear as quasi-horizontal flow fields, with a vertical ‘wavelength’ that tends to zero. As such, they must be expected to induce secondary shear instabilities and cascade into motions of smaller (horizontal) scale.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 1 , 16 January 1979 , pp. 1 - 19
Copyright
© 1979 Cambridge University Press

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