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On the role of vortex stretching in energy optimal growth of three-dimensional perturbations on plane parallel shear flows

Published online by Cambridge University Press:  19 July 2012

H. Vitoshkin ,
E. Heifetz ,
A. Yu. Gelfgat  and
N. Harnik
H. Vitoshkin*
Affiliation:
School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
E. Heifetz
Affiliation:
Department of Geophysics, Atmospheric and Planetary Sciences, Tel Aviv University, Tel Aviv 69978, Israel
A. Yu. Gelfgat
Affiliation:
School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
N. Harnik
Affiliation:
Department of Geophysics, Atmospheric and Planetary Sciences, Tel Aviv University, Tel Aviv 69978, Israel
*
†Email address for correspondence: [email protected]
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Abstract

The three-dimensional linearized optimal energy growth mechanism, in plane parallel shear flows, is re-examined in terms of the role of vortex stretching and the interplay between the spanwise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille and mixing-layer shear profiles is robust and resembles localized plane waves in regions where the background shear is large. The waves are tilted with the shear when the spanwise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification affects the optimal energy growth. This perspective provides an understanding of the three-dimensional growth solely from the two-dimensional dynamics on the shear plane.

JFM classification

Waves/Free-surface Flows: Shear waves Vortex Flows: Vortex instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 707 , 25 September 2012 , pp. 369 - 380
Copyright
Copyright © Cambridge University Press 2012

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