Roughness sublayer in non-equilibrium wall-bounded turbulence

In rough-wall turbulent flows, the roughness sublayer (RSL) is the near-wall layer where roughness modifies directly the flow dynamics. Despite the importance of this layer in non-equilibrium flows, such as those with strong pressure gradients, the dynamics inside the RSL are not well understood. Direct and large-eddy simulation data are used to show evidence that the RSL thickness and velocities appear to behave as if in a quasi-equilibrium state, in both accelerating and decelerating flows. For example, in an attached flat-plate boundary layer with strong adverse pressure gradient, the wall friction normalized by the RSL edge velocity stays almost constant, while it does not scale on the boundary layer edge velocity. The same scaling is observed for wall friction and form-induced stresses in transient accelerated turbulent channel flows. This is possibly because, although the mean pressure gradient directly accelerates the mean velocity, it is not present in the transport equation of the form-induced velocity. The observed self-preservation in RSL is encouraging for coarse-grained modeling approaches (e.g. RANS and wall-modeled LES) as it implies that equilibrium or quasi-steady RSL models may be applicable to transient and spatial developing flows, though this hypothesis needs to be tested over a wide range of pressure gradient, Reynolds number and roughness topography.