Properties of the kinetic energy budgets in wall-bounded turbulent flows

Abstract

Available high-quality numerical simulation data are used to investigate and characterize the kinetic energy budgets for fully developed turbulent flow in pipes and channels, and in the zero-pressure gradient turbulent boundary layer. The mean kinetic energy equation in these flows is empirically and analytically shown to respectively exhibit the same four-layer leading-order balance structure as the mean momentum equation. This property of the mean kinetic energy budget provides guidance on how to group terms in the more complicated turbulence and total kinetic energy budgets. Under the suggested grouping, the turbulence budget shows either a two- or three-layer structure (depending on channel or pipe versus boundary layer flow), while the total kinetic energy budget exhibits a clear four-layer structure. These layers, however, differ in position and size and exhibit variations with friction Reynolds number (δ+) that are distinct from the layer structure associated with the mean dynamics. The present analyses indicate that each of the four layers is characterized by a predominance of a reduced set of the grouped terms in the governing equation. The width of the third layer is mathematically reasoned to scale like δ+-δ+ at finite Reynolds numbers. In the boundary layer the upper bounds of both the second and third layers convincingly merge under this normalization, as does the width of the third layer. This normalization also seems to be valid for the width of the third layer in pipes and channels, but only for δ+>1000. The leading-order balances in the total kinetic energy budget are shown to arise from a nontrivial interweaving of the mean and turbulence budget contributions with distance from the wall.