Understanding and modeling the roughness sublayer in non-equilibrium turbulent flows

The roughness sublayer (RSL) is the near-wall region of a rough-walled turbulence that is dynamically important in non-canonical flows but not well-understood. This work first summarizes recent findings on the RSL flow in non-equilibrium flat-plate boundary layers subject to strong favorable or adverse streamwise pressure gradients based on large-eddy simulations. It is shown that several mean flow quantities in the RSL stay invariant despite the strong pressure gradients, when they are normalized with a set of sublayer velocity and length scales. These quantities include the constant RSL thickness, constant hydrodynamic drag, and self-similar mean velocity and dispersive stresses. However, the Reynolds stresses normalized this way are not self-similar in the RSL. But the weak equilibrium criterion is satisfied as the Reynolds-stress anisotropy is invariant. Some of these observations appear to apply to flow sections with high local roughness Reynolds number only. Incorporation of the scaling relation into turbulence closures for rough-walled flows will be discussed.