Towards Modelling the Downstream Development of a Turbulent Boundary Layer Following a Rough-to-Smooth Step Change in Surface Condition*

In this study we examine the effect of both the friction Reynolds number $Re_{\tau}$ and the roughness Reynolds number $k_s^+$ on a turbulent boundary layer following a rough-to-smooth step change in surface condition along the flow direction. To investigate the effect of $Re_{\tau}$, a set of wind-tunnel experiments is conducted at $k_s^+=160$ while $Re_{\tau}$ is varied from 7100 to 21000. Similarly, to examine the dependence on $k_s^+$, a set of measurements is conducted at $Re_{\tau}=14000$ with $k_s^+$ ranging from 110 to 230. Hot-wire profiles are obtained on a logarithmically spaced grid up to 120 boundary-layer thicknesses downstream of the step change, and the local wall-shear stress is measured directly using oil-film interferometry. Using these data, we propose a new model of the recovering mean velocity profile which accounts for the well-known non-equilibrium behaviour of the internal layer. This mean velocity distribution is then evolved downstream of the step change using the integrated streamwise momentum equation to achieve a full prediction of the mean flow recovery.