Journal of Fluid Mechanics

A note on an algebraic instability of inviscid parallel shear flows

M. T.  Landahl a1
a1 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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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.

(Published Online April 19 2006)
(Received December 28 1978)
(Revised September 17 1979)