Near-wall characteristics of non-equilibrium turbulent boundary layers on rough walls

Abstract

Engineering models of rough-wall turbulent flows rely on reduced model of the near-wall layer of flow modified by roughness (i.e. the roughness sublayer) to provide boundary conditions to the flow above. Understanding sublayer response to pressure gradients and the pressure gradient history is crucial for developing physics-based turbulence closures. This work examines characteristics of the roughness sublayer using roughness-resolved simulation data of two flat-plate boundary layers: one direct numerical simulation with strong non-equilibrium favorable pressure gradients (Yuan and Piomelli, 2015) and a large-eddy simulation with a suction-blowing freestream that induces both adverse and favorable pressure gradients. The sublayer thickness $y_R$ is found to be constant in attached-flow regions, regardless of pressure gradients. When using a set of sublayer scales ($U_R$, $y_R$) for normalization (where $U_R$ is the local streamwise mean velocity at the elevation $y_R$), an overall self-similarity is observed for the total drag, mean velocity, and dispersive stresses inside the sublayer, suggesting that the time-mean flow is in quasi-equilibrium despite varying pressure gradients. For the Reynolds stress profiles, self-similarity under the present normalization is not present in general, but the Reynolds stress anisotropy appears to satisfy the weak-equilibrium condition. The observed invariance properties of the roughness sublayer flow indicate potential for extending existing sublayer-unresolved turbulence models to rough-wall non-equilibrium flows and provide a way to assess existing roughness treatments in turbulence models.