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A note on an algebraic instability of inviscid parallel shear flows

Published online by Cambridge University Press:  19 April 2006

M. T. Landahl
M. T. Landahl
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. and Department of Mechanics, The Royal Institute of Technology, Stockholm, Sweden
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Abstract

It is shown that all parallel inviscid shear flows of constant density are unstable to a wide class of initial infinitesimal three-dimensional disturbances in the sense that, according to linear theory, the kinetic energy of the disturbance will grow at least as fast as linearly in time. This can occur even when the disturbance velocities are bounded, because the streamwise length of the disturbed region grows linearly with time. This finding may have implications for the observed tendency of turbulent shear flows to develop a longitudinal streaky structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 2 , 29 May 1980 , pp. 243 - 251
Copyright
© 1980 Cambridge University Press

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