Modified hierarchy structure of rough-wall flows

Abstract

Analysis of the mean differential force balance reveals that the characteristic properties of wall-bounded turbulent flows (e.g., the logarithmic mean profile and distance-from-the-wall scaling) arise owing to the existence of an internal layer hierarchy. Mathematically, this hierarchical structure is formally admitted by the appropriately simplified Reynolds Averaged Navier-Stokes (RANS) equation. Physically, its existence accounts for the dynamics undergoing a continuous self-similar (approximately) variation in scale over the range ν/uτ ≤ ℓ ≤ δ. These findings lead to the hypothesis that surface roughness modifies this mean dynamical structure through the imposition of new length scales. ..