Turbulent drag reduction via oblique travelling waves.

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Luca Marchesani

The present study describes the response of a turbulent channel flow to sinu- soidal travelling waves of spanwise velocity applied at the walls. The waves travel along oblique directions between the streamwise and the spanwise extrema, resulting in: oblique travelling waves. These boundary phenomena have been studied by Quadrio et al. (J. Fluid Mech., 627, 2009) and Zhao et al. (Fluid Dyn. Res., 34, 2004) respectively. The former is nowadays considered as one of the most promising open-loop strategies for turbulent skin-friction drag reduction.

The effect of the travel direction of the waves upon the drag reduction and the consequent net energy savings is studied through Direct Numerical Simulations: a parametric campaign has been carried out in order to fully investigate the whole parameter space, by simultaneously changing: the amplitude A, the temporal frequency omega and the streamwise and spanwise wavenumber components kx and kz.

The results from more than 2000 DNS assess that, at any amplitude, the optimal forcing, either in terms of drag reduction and net energy saving, is always the one with kz = 0. In other words, it is not possible to im- prove the streamwise-travelling waves described by Quadrio et al.