Turbulent Channel Flow over Model “Dynamic” Roughness

Abstract

Turbulent flow over a “dynamically rough” wall is modeled by considering time-dependent velocity perturbations in the streamwise and wall-normal directions imposed at the wall, a crude linearization. Analysis of the linearized Navier-Stokes operator is performed to select roughness parameters that are predicted to lead to a large disturbance amplification in the body of the flow. Direct numerical simulations of turbulent channel flow at Re _τ ∼ 500 with three different roughness amplitudes, a ⁺, indicate that for ${a}^{+}\,=\,10$ the response of the flow approximates this predicted form, including the development of a significant spanwise velocity component. The turbulence characteristics, as a function of amplitude, are hypothesized to offer insight of relevance to the static roughness problem.