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

Published online by Cambridge University Press:  14 October 2021

Axel Deloncle ,
Jean-Marc Chomaz  and
Paul Billant
Axel Deloncle
Affiliation:
LadHyX, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, Franceaxel.deloncle@ladhyx.polytechnique.fr
Jean-Marc Chomaz
Affiliation:
LadHyX, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, Franceaxel.deloncle@ladhyx.polytechnique.fr
Paul Billant
Affiliation:
LadHyX, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, Franceaxel.deloncle@ladhyx.polytechnique.fr
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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 ∞ 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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 297 - 305
Copyright
Copyright © Cambridge University Press 2007

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