Scaling for Turbulent Flows Encountering Roughness Transitions*

Roughness transitions in turbulent flows are widespread in nature and technology -- where ocean meets land, patchy bio-fouling on naval vessels, or deterioration of turbine blades. In such flows, an internal boundary layer (IBL) forms at the point of transition. The IBL introduces an unsteady region to the flow, as well as new time- and length-scales. This growing region complicates the scaling of these flows, as the IBL prevents mean velocity profiles from exhibiting self-similarity.

In this talk, we will discuss the capability of scaling parameters based on IBL characteristics, using simulation and experimental data. We supplement our wall-modeled large-eddy simulation (WMLES) data with two publicly available experimental datasets, covering the full range of surface transition types (smooth-to-rough, rough-to-smooth, rough-to-rougher, and vice versa), from Re_τ ~ O(10³-10⁶). We find the IBL height δ_i and the edge velocity U_i collapse profiles of the mean velocity and velocity defect within the IBL. This allows for a quasi-equilibrium treatment to this unsteady region of the flow.