Three-dimensional instability of shear flows with inflection-free velocity profiles in stratified media with a high Prandtl number |
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Authors: | S M Churilov |
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Institution: | 1.Institute of Solar-Terrestrial Physics, Siberian Branch,Russian Academy of Sciences,Irkutsk,Russia |
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Abstract: | In stably stratified media with a Prandtl number Pr ≫ 1, vertical scales of the density (ℓ) and horizontal velocity variation (L) are quite different, ℓ/L = O(Pr−1/2) ≪ 1, and this influences the flow stability. In particular, shear flows without inflection points on the velocity profile
are unstable even in an ideal incompressible fluid. The maximum instability growth rate for sufficiently small ℓ/L is of the same order as in homogeneous mixing layers, with mainly three-dimensional rather than two-dimensional oscillations
increasing in a wide range of parameters. This paper focuses on the three-dimensional instability of such flows. It is shown
that the spectrum of unstable oscillations is essentially anisotropic in the case of a relatively weak stratification when
the bulk Richardson number J ≤ O(ℓ/L)3/2]. The results of the asymptotic analysis are illustrated by calculations for a model flow in a two-layer medium (ℓ = 0) as well as for flows with values of ℓ/L corresponding to a temperature or salinity stratification of the water. |
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