Harmonic oscillations of the walls of a turbulent plane channel flow are
studied by direct numerical simulations to improve our understanding of the
physical mechanism for skin-friction drag reduction. The simulations are
carried out at constant pressure gradient in order to define an unambiguous
inner scaling: in this case, drag reduction manifests itself as an increase of
mass flow rate. Energy and enstrophy balances, carried out to emphasize the
role of the oscillating spanwise shear layer, show that the viscous
dissipations of the mean flow and of the turbulent fluctuations increase with
the mass flow rate, and the relative importance of the latter decreases. We
then focus on the turbulent enstrophy: through an analysis of the temporal
evolution from the beginning of the wall motion, the dominant,
oscillation-related term in the turbulent enstrophy is shown to cause the
turbulent dissipation to be enhanced in absolute terms, before the slow drift
towards the new quasi-equilibrium condition. This mechanism is found to be
responsible for the increase in mass flow rate. We finally show that the
time-average volume integral of the dominant term relates linearly to the drag
reduction
