Large-scale instabilities of turbulent wakes

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Abstract
The equations describing the statistical features of small amplitude waves in a turbulent shear flow are derived from the Navier-Stokes equations. Closure is achieved through a postulated constitutive equation for the alteration of the statistical properties of the turbulence by the organized wave. The theory is applied in an examination of the stability of a hypothetical wake consisting of small-scale turbulence enclosed within a steady uncontorted superlayer. A set of superlayer jump conditions is derived from fundamental considerations, and these are of more general interest. For this hypothetical flow the analysis predicts largescale instabilities and superlayer contortions reminiscent of large-eddy structures observed in real flows. These instabilities therefore offer an explanation of the presence of large-scale organized motions in turbulent free shear flows.