A theoretical model for coherent structures in wall turbulence

An inviscid model for a large-scale coherent structure of boundary layer turbulence is developed, which is based on the hypothesis that large-scale motion is initiated by the collective effects of short-lived small-scale Reynolds stresses produced by local secondary instability. Statistical model equations for the coherent structure were obtained by the application of conditional sampling of the inviscid equations, under the assumption that the sampled small-scale Reynolds stresses are short-lived and have a Gaussian distribution in the streamwise direction over a distance that is large compared to the thickness of the stress-producing region. The interaction of the large-scale motion with the mean shear is shown to produce a local internal shear layer, which intensifies and extends in the streamwise direction as it moves downstream. The mechanism involved in the shear intensification is identified as the stretching of the mean vorticity by the spanwise perturbation velocities.