Large-eddy simulation of turbulent boundary-layer flow through a rough-smooth wall-surface transition

We describe results from a large-eddy-simulation (LES) study of a zero-pressure gradient, flat-plate turbulent boundary layer that flows across a discontinuous, span-wise, rough-smooth, wall-surface transition. The virtual-wall model of Saito and Pullin (PoF, 2012) is utilized to model subgrid-scale roughness by use of the Colebrook form of the roughness function $\Delta U^+(k_s^+)$, where $k_s^+ = k_s\,u_\tau/\nu$ and $k_s$ is the equivalent sand-grain roughness. For given $Re_\tau = \delta_0\,u_\tau/\nu$ and ratio of $k_s$ to the boundary layer thickness at the transition $k_s/\delta_0$, the variation of $C_f(x)$ through the surface transition is calculated dynamically from the LES. Results at $Re_\tau\approx 4000$ are compared with detailed measurements for rough-smooth transition obtained at the University of Melbourne. The LES is used to explore the scaling behaviour of the discontinuity in $C_f$ at the transition and also the relaxation of $C_f(x)$ to appropriate downstream, equilibrium conditions (and any dependence on $Re_\tau$ and $k_s/\delta_0$).