Scale-Dependent Energy Fluxes in a Rough-Wall Turbulent Channel Flow

Abstract

In this paper, we investigate the characteristics of energy fluxes within rough-wall turbulent boundary layer at different scales in the context of large eddy simulations (LES) utilizing high resolution Particle Image Velocimetry (PIV) data obtained in an optically index-matched facility. The rough surface consists of closely-packed pyramidal elements, and the measurement region includes the entire roughness sublayer and lower portion of outer-layer with a vector resolution of ∼9 wall units and 14% of roughness height. Our recent study has demonstrated that the entire boundary layer is flooded with an excessive number of roughness-scale eddies that are generated near the wall and advected away from it by large scale coherent structures present in the outer layer. Following this observation, the original velocity field is spatially filtered using 2D top-hat filter of length scale Δ = 1k, 3k, 6k (k is roughness height) that represent roughness, intermediate and large scale motions, respectively. In these ranges, the subgrid scale (SGS) energy fluxes show substantial increase with scale and with decreasing distance from the wall. The latter trend persists even when fluxes are scaled with the local TKE production rate. When the fluxes are decomposed to local and non-local contributions, they show a scale-dependent near-wall increase of energy transfer which bypasses the typical cascading process. This non-local flux is even larger than the local one near the wall for the [k, 3k] range. These trends are attributed to interactions of large scale turbulence with the wall roughness and the abundant roughness scale eddies near the wall. The paper also examines the behavior of Smagorinsky model coefficients, and show scale-dependence when trends at filter scales of 1k and 3k are compared to those at 6k. Both dissipation based and dynamic model coefficients show very little variation with height as long as the filter scale is in the 1–3k range, but increase with elevation for Δ = 6k.