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Stability of non-planar shear flow of a stratified fluid

Published online by Cambridge University Press:  29 March 2006

William Blumen
William Blumen
Affiliation:
Department of Astro-Geophysics, University of Colorado, Boulder
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Abstract

The linear stability of non-planar shear flow of a stably stratified fluid is investigated. Howard's (1961) semicircle theorem, which places bounds on the range of the complex phase speed c, is derived, although sufficient conditions for stability of the (x-directed) basic flow $\overline{u}(y, z)$ have not been established. The stability properties of some particular shear-layer and jet flows for long-wave disturbances are examined. Much of the effort is directed to delineation of unstable properties of the flow $\overline{u}(y, z) = \tan h\,y \tan h\,z$ in terms of c, the wavenumber α and a local form J0, of the Richardson number. Limiting cases are inflexion-point instability (J0 = ∞) and two-dimensional instability of a vertically stratified shear flow ($J_0 < \frac{1}{4}$). The present numerical computations reveal that at least two modes of instability are present for each pair of values of α and J0 for α [les ] 0·2 and $J_0 < \frac{1}{4}$. The source of instability for each mode is examined by means of computed energy transformations. However, numerical difficulties prevent a detailed examination of these unstable modes for α > 0·2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 1 , 11 March 1975 , pp. 177 - 189
Copyright
© 1975 Cambridge University Press

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