Minimal-span direct simulation of~transient, accelerating channel flows and application with wall riblets.*

Minimal-span simulation of wall~turbulence is an attractive approach for reducing simulation~cost~when~focusing~on~near-wall~phenomena~~associated with frictional drag modification due to surface riblets~or roughness. We~evaluate the capability~of~such~simulations~for~a periodic smooth-wall channel flow subjected to~rapid~acceleration from a friction Reynolds number of 180 to one of 420. Compared to a~full-span simulation, the single-point statistics, two-point correlations and~spectral analyses~indicate that the minimal span is sufficient to capture the~pseudo-laminarization phenomenon, since the stabilization effect of the increased~ensemble-averaged shear is~confined to~the near-wall region. As the increased shear is relaxed, the~retransition to a new equilibrium state, though starting from the wall, is slightly~delayed~compared to that in a full channel.~The wall is~then covered with saw-tooth riblets of a uniform height, which is 7.5~wall units at the start of, and 17.5 at the end of acceleration. Lower Reynolds~stresses (in wall units) and a~slower retransition are observed in the riblet flow, compared to a smooth-wall channel flow.~The results demonstrate both advantages and~limitations of minimal-span~simulations of non-equilibrium wall turbulence.