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Spatial stability of horizontally sheared flow

Pages: 611 - 618, Issue special, November 2013

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Iordanka N. Panayotova - Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, United States (email)
Pai Song - Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, United States (email)
John P. McHugh - Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, United States (email)

Abstract: We investigate the stability of a shear flow in a stratified fluid. The flow is assumed to be inviscid and Boussinesq and the base state density gradient is vertical with constant Brunt-Vaisala frequency. The shear is taken as horizontal, where the base-state velocity has uniform direction and it's magnitude depends on the transverse horizontal coordinate, U(y). Unlike vertical shear flows, this combination of horizontal shear with vertical stratification is inherently three-dimensional and Squire's theorem is inapplicable. Spatial stability characteristics are obtained using the normal-mode approach and the Riccati transform. Sensitivity of the stability characteristics and their qualitative features are investigated by numerical methods for free-shear flow approximated by the hyperbolic tangent.

Keywords:  Spatial stability, horizontal shear flow, Riccati equation, unstable shear flow.
Mathematics Subject Classification:  Primary: 76F10; Secondary: 76E05.

Received: August 2012;      Revised: January 2013;      Published: November 2013.

 References