The streamwise drag-reduction response of a boundary layer subjected to a sudden imposition of transverse oscillatory wall motion

Abstract

A direct numerical simulation study is presented, which examines the response of a spatially developing boundary layer to oscillatory spanwise wall motion imposed over a limited streamwise stretch. At the heart of the study is the dependence of the streamwise variations in skin friction and turbulence properties on the period of the oscillatory motion, with particular emphasis placed on the behaviour downstream of the start of the actuation. The friction Reynolds number just upstream of the actuation is Reτ = 520, and the wall-scaled actuation period, T+ = Tuτ2/ν, covers the range 80–200. In contrast to channel flow, the present configuration allows the processes during the transition stretch from the unactuated state to the low-drag state and the recovery from the low-drag state to be studied. Attention focuses primarily on the former. Results are included for the time-averaged turbulent stresses, their budgets and probability-density functions, as well as a range of phase-averaged properties. The study brings out, for low-drag conditions, a number of features and processes that are common with those in actuated channel flow, but suggests that the maximum drag-reduction margins are lower than those in equivalent channel flow, and that the optimum actuation period is significantly shorter. The transition to the low-drag state occurs over about 5 boundary-layer thicknesses, and is characterised by substantial oscillations in all phase-averaged properties. These oscillations, provoked at the start of the spanwise motion, propagate convectively as waves and decay as the low-drag state is approached. The interactions contributing to the oscillations are discussed as part of the analysis of phase-averaged quantities.