Reynolds number effects on scale energy balance in wall turbulence

The scale energy budget utilizes a modified version of the classical Kolmogorov equation of wall turbulence to develop an evolution equation for the second order structure function [R. J. Hill, "Exact second-order structure-function relationships," J. Fluid Mech. 468 , 317 (2002)]. This methodology allows for the simultaneous characterization of the energy cascade and spatial fluxes in turbulent shear flows across the entire physical domain as well as the range of scales. The present study utilizes this methodology to characterize the effects of Reynolds number on the balance of energy fluxes in turbulent channel flows. Direct numerical simulation data in the range Re τ =300-934 are compared to previously published results at Re τ =180 [N. Marati, C. M. Casciola, and R. Piva, "Energy cascade and spatial fluxes in wall turbulence," J. Fluid Mech. 521 , 191 (2004)]. The present results show no Reynolds number effects in the terms of the scale energy budget in either the viscous sublayer or buffer regions of the channel. In the logarithmic layer, the transfer of energy across scales clearly varies with Reynolds number, while the production of turbulent kinetic energy is not dependent on Reynolds number. An envelope of inverse energy cascade is quantified in the buffer region within which energy is transferred from small to larger scales. This envelope is observed in the range 6< y +