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Three-dimensional stability of a horizontally sheared flow in a stably stratified fluid

Abstract : This paper investigates the three-dimensional stability of a horizontal flow sheared horizontally, the hyperbolic tangent velocity profile, in a stably stratified fluid. In an homogeneous fluid, the Squire theorem states that the most unstable perturbation is two-dimensional. When the flow is stably stratified, this theorem does not apply and we have performed a numerical study to investigate the three-dimensional stability characteristics of the flow. When the Froude number, Fh, is varied from 8 to 0.05, the most unstable mode remains two-dimensional. However, the range of unstable vertical wavenumbers widens proportionally to the inverse of the Froude number for Fh " 1. This means that the stronger the stratification, the smaller the vertical scales that can be destabilized. This loss of selectivity of the two-dimensional mode in horizontal shear flows stratified vertically may explain the layering observed numerically and experimentally. © 2007 Cambridge University Press.
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Axel Deloncle, Jean-Marc Chomaz, Paul Billant. Three-dimensional stability of a horizontally sheared flow in a stably stratified fluid. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2007, 570 (January), pp.297-305. ⟨10.1017/s0022112006003454⟩. ⟨hal-01023344⟩

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