Large eddy simulation of smooth–rough–smooth transitions in turbulent channel flows

We describe a high Reynolds number large-eddy-simulation (LES) study of turbulent flow in a long channel of length 128 channel half heights, δδ, with the walls consisting of roughness strips where the long stream-wise extent invites a full relaxation of the mean velocities within each strip. The channel is stream-wise periodic and strips are oriented transverse to the flow resulting in repeated transitions between smooth and rough surfaces along the stream-wise direction. The present LES uses a wall model that contains Colebrook’s empirical formula as a roughness correction to both the local and dynamic calculation of the friction velocity and also the LES wall boundary condition. This operates point-wise across wall surfaces, and hence changes in the outer flow can be viewed as a response to the temporally and/or spatially variant roughness distribution. At the wall surface, dynamically calculated levels of time- and span-wise-averaged friction velocity uτ‾(x) over/undershoot and then fully recover towards their smooth or rough state over a stream-wise distance of order 10–30 δδ depending on both roughness and Reynolds number. Also, the initial response rate in uτ‾ shows Reynolds number and roughness dependence over both transitions. The growth rate of the internal boundary layer (IBL), defined by the abrupt change in stream-wise turbulent intensity, is found to grow as x0.70x0.70 on average over multiple simulation conditions for the case of a smooth-to-rough transition, which agrees with the experimental results of Antonia and Luxton (1971) [1] and Efros and Krogstad (2011) [2]. IBL profiles demonstrate a good collapse on δ/log(Reτ∗), where Reτ∗ is the local Reynolds number based on uτ‾ at the point of full recovery.