In an effort to isolate the mechanism by which streamwise structures form in turbulent wall layers, evolution equations were derived for the streamwise velocity and vorticity perturbations about a mean turbulent shear flow. ‘Mean’, of course, implies an average and the form of average is most important. One serious candidate is Reynolds-Hussain averaging, but because the instantaneous velocity is broken into mean, periodic and fluctuating components, difficulties arise in specifying terms which result from phase averages of fluctuating velocities and time averages of phase velocities. Such problems are less acute if the Generalized Lagrangian mean (GLM) equations of Andrews fc McIntyre (1978) are employed and that is the approach taken. The GLM formulation — which is an exact mapping of the Navier Stokes equation —was constructed with wave/mean flow interactions in mind. In turbulent flow, however, the wave field is not explicit but exists as feedback from the the global or rectified effect of turbulence fluctuations throughout the layer. The net effect of this implicit wave field is captured formally in terms of space-time correlations at convection delay through two vector quantities, the Stokes drift and the pseudomomentum. Since these correlations have, for the most part, been measured, the resulting nonlinear evolution equations may be closed by appeal to experiment.
KeywordsShear Layer Navier Stoke Equation Streamwise Velocity Nonlinear Evolution Equation Streamwise Vortex