Analysis of Instantaneous Turbulent Velocity Vector and Temperature Profiles in Transitional Rough Channel Flow

Abstract

The instantaneous velocity vector and instantaneous temperature in a turbulent flow in a transitionally rough channel have been analyzed from unsteady Navier–Stokes equations and unsteady thermal energy equation for large Reynolds numbers. The inner and outer layers asymptotic expansions for the instantaneous velocity vector and instantaneous temperature have been matched in the overlap region by the Izakson–Millikan–Kolmogorov hypothesis. The higher order effects and implications of the intermediate (or meso) layer are analyzed for the instantaneous velocity vector and instantaneous temperature. Uniformly valid solutions for instantaneous velocity vector have been decomposed into the mean velocity vector, and fluctuations in velocity vector, as well as the instantaneous temperature, have been decomposed into mean temperature and fluctuations in temperature. It is shown in the present work that if the mean velocity vector in the work of Afzal (1976, “Millikan Argument at Moderately Large Reynolds Numbers,” Phys. Fluids, 16, pp. 600–602) is replaced by instantaneous velocity vector, we get the results of Lundgren (2007, “Asymptotic Analysis of the Constant Pressure Turbulent Boundary Layer,” Phys. Fluids, 19, pp. 055105) for instantaneous velocity vector. The comparison of the predictions for momentum and thermal mesolayers is supported by direct numerical simulation (DNS) and experimental data.