An iterative method to link surface roughness and turbulent mean-flow response using resolvent analysis

A physics-based model is developed to predict the spatially varying sensitivity of turbulence to roughness geometry and the corresponding flow modifications. Resolvent analysis with a drag-normalized, Reynolds-decomposed volume penalization is formulated to efficiently link the mean flow profile to predictions of the drag force, wake field fluctuations, and dispersive stresses for broadband (sandgrain) surface roughness. An eddy viscosity approach models the modification of the stochastic stress arising due to the attenuation of convecting fluctuations within the roughness sublayer. Crucially, these components link the mean-flow profile to the force profiles and stresses which determine its shape, so that the model can be iteratively solved for a given bulk flow over a surface roughness, starting from an initial corresponding smooth wall flow condition. For engineering-relevant surface geometries in flows which respect outer similarity, the model output estimates turbulent-drag response, namely equivalent sandgrain roughness, Hama roughness-function and spatial variation of roughness sublayer (wake field) turbulent fluctuations. The approach is demonstrated on a channel flow with sandgrain roughness at an engineering-relevant Reynolds number.