Turbulence in plane channel flows

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Abstract
This paper complements an earlier study of the mean velocities in turbulent flows in a flat channel, one of whose walls can move relative to the other, so that the role of the stress gradient within the wall layers can be varied widely and in a controlled manner.Measurements of longitudinal, normal and lateral velocity fluctuation intensities (u′,v′,w′) and of shear stresses have been made in essentially fully developed flows established by various combinations of pressure gradient and wall velocity The channel aspect ratio (breadth/height) has been varied between 12 and 28 and the development ratio (development length/height) between 20 and 45. The introduction of a turbulence-generating grid at the entrance to the duct increases the effective development length.The study has considered twenty-six flows that are two-dimensional in the mean, which have been established by blowing and relative motion either in the same direction or directly opposed. Empirical descriptions, based on similarity laws incorporating either the wall stress or the local stress, are developed for the turbulence near the walls and in the core. The profiles of u′, v′ and w′ coalesce, to a reasonable approximation, when normalized with appropriate length and velocity scales. Extensive ‘plateau’ regions are identified, in which the scaled intensities are sensibly constant.A number of quantities characteristic of the structure of the turbulence are considered, in order to elucidate the effect of the stress gradient on the wall layer, and stages in the erosion of the constant-stress layer are identified.