Influence of large-scale motions on the frictional drag in a turbulent boundary layer

Abstract

Direct numerical simulation data of a turbulent boundary layer (Re-tau = 1000) were used to investigate the large-scale influences on the vortical structures that contribute to the local skin friction. The amplitudes of the streamwise and wall-normal swirling strengths (lambda(x) and lambda(y)) were conditionally sampled by measuring the large-scale streamwise velocity fluctuations (u(l)). In the near-wall region, the amplitudes of lambda(x) and lambda(y) decreased under negative ul rather than under positive u(l) . This behaviour arose from the spanwise motions within the footprints of the large-scale low-speed (u(l) < 0) and high-speed structures (u(l) > 0). The intense spanwise motions under the footprint of positive u(l) noticeably strengthened the small-scale spanwise velocity fluctuations (w(s)) below the centre of the near-wall vortical structures as compared to w(s) within the footprint of negative u(l) . The streamwise and wall-normal components were attenuated or amplified around the modulated vortical motions, which in turn led to the dependence of the swirling strength on the u(l) event. We quantified the contribution of the modulated vortical motions <-w omega(y)>, which were related to a change-of-scale effect due to the vortex-stretching force, to the local skin friction. In the near-wall region, intense values of <-w omega(y)> were observed for positive u(l) . By contrast, these values were low for negative u(l) , in connection with the amplification of w(s) and lambda(y) by the strong spanwise motions of the positive u(l) . The resultant skin friction induced by the amplified vortical motions within u(l)(+) > 2 was responsible for 15% of the total skin friction generated by the change-of-scale effect. Finally, we applied this analysis to a drag-reduced flow and found that the amplified vortical motions within the footprint of positive u(l) were markedly diminished, which ultimately contributed to the total drag reduction.