TURBULENT VELOCITY PROFILES FROM STABILITY-CRITERIA

A velocity-defect law for channel flow is shown to result from the single requirement of Reynolds-stress spectral ‘smoothness’ for any mean profile maintained free of inflexions by transient instabilities. The deduced velocity is a logarithmic function of position near boundaries and parabolic in mid-regions of the flow, independent of the detailed mechanisms of momentum transport by the fluid. However, if the ‘smoothness’ of the spectral tail is decreased, a second logarithmic layer of steeper slope emerges inside the first layer. Profile data from drag-reduction experiments gathered by Virk (1975) exhibit the deduced inner log layer and its transition region to the usual outer flow. © 1979, Cambridge University Press. All rights reserved.