On sublayer streaks

Abstract

Turbulent sublayer streaks are studied with the aid of a simplified theoretical model. In this the nonlinear activity is assumed to be intermittent and to act locally in space during a very short initial time so as to set up the initial conditions for the subsequent linear and inviscid evolution of the resulting three-dimensional flow disturbance. The mean shear flow is taken as a parallel one and a correction for the long-tern effects of viscosity is applied. A model for the initial nonlinear phase is chosen to represent the local Reynolds stresses that would be produced by a patch of local inflectional instability. The streamwise dimension of the resulting eddy is found to grow linearly with time in accordance with the algebraic instability mechanism (Landahl 1980). The associated Reynolds shear stress is expressible in a simple manner in terms of the liftup of the fluid elements and is suggestive of an algebraic-type Reynolds stress model similar to, but not identical to, that of Prandtl's (1925) mixing-length theory.