Simulations of non-equilibrium rough-wall flows

This integrated report catalogs the response of different rough surfaces in rough-to-smooth (RTS) channel flow configurations. Two types of roughness shapes are investigated using direct numerical simulations (DNS): square bars aligned in a direction transverse to the flow and cubes arranged in a staggered manner. The underlying motivations are four fold: to provide accurate data on statistical and structural state of turbulence in RTS configurations; to expand on previous experimental studies; to determine the recovery rate and longitudinal distances required to attain the asymptotic states; and to contrast the differences in adjustment between different rough walls. The frictional Reynolds number, $Re_{\tau}$, at the different rough walls ranges between $1500-2500$, while at the smooth wall it reduces to around 920. The effective sand-grain lengthscale, $k_s^+=300-2100$, falls within the fully-rough regime. The gross recovery $-$ particularly in the outer regions of the flow where it is of the order of $50\delta$ $-$ is slow and incomplete by the streamwise exit of the computational domains, at $x/\delta \approx 10$. Skin friction profiles after the step change in roughness decrease below the smooth-wall level due to the sudden expansion of the mean flow. This expansion also produces strong advection in the developing regime. The skin friction then recovers rapidly and essentially levels off at the level of the fully developed smooth-wall by $x/\delta=1-2$. The pressure gradient at the wall, however, stays slightly adverse for most of the streamwise extent of the non-equilibrium wall, only becoming favourable at $x/\delta\u3e5$. Other statistics demonstrate comparatively quick adjustment by $x/\delta=1$ to a `near\u27 equilibrium state close to the wall. This is a consequence of strong mean shear emerging immediately after the change in surface condition. The term `near\u27 equilibrium implies similar profile shapes and identical vertical locations of local features to those for fully developed flows; magnitude of these features could be higher. The penetrations at the wall by roughness induced large-scales is the difference between `near\u27 and complete equilibrium, and this is ultimately responsible for incomplete recovery even within the inner layer. Flow visualizations reveal immediate appearance of elongated streamwise streaks, which are characteristic of turbulent smooth walls, after the abrupt change in shear at the wall. Disturbances by large structures emanating from the outer layer, however, cause a thickening of the turbulence structure in the inner layer. The absence of a logarithmic region is attributed to the aforementioned advection, and approximate curve-fits estimate their relaxation at $x=15-20\delta$. The dominant momentum balance in the developing flow within the extent of the computational domains is between advection and turbulence fluxes, while pressure fluxes are much smaller. These strong momentum fluxes are directly influenced by the upstream rough surfaces. The high TKE dissipation rate, $\epsilon$, above the rough wall decays rapidly upon the transition as roughness induced small scales disappear. Even so, $\epsilon$ remains significantly higher than that at the fully developed smooth wall and relaxes slowly with downstream fetch. This higher level of $\epsilon$ is arguably associated with higher levels of large-scale TKE from the upstream rough walls cascading down towards dissipation length-scales. A statistically stationary state exists at the upper smooth wall albeit at a higher $Re_{\tau}$ than that observed for equivalent channels where both walls are smooth. This is attributed to a different bulk flow as seen from this wall, i.e. a smaller $\delta_U$. Absence of streamwise development at this wall is due to a negligible change in mean shear