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

  • Jinyul Hwang (a1) and Hyung Jin Sung (a1)

Direct numerical simulation data of a turbulent boundary layer ( $Re_{\unicode[STIX]{x1D70F}}=1000$ ) 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 ( $\unicode[STIX]{x1D706}_{x}$ and $\unicode[STIX]{x1D706}_{y}$ ) were conditionally sampled by measuring the large-scale streamwise velocity fluctuations ( $u_{l}$ ). In the near-wall region, the amplitudes of $\unicode[STIX]{x1D706}_{x}$ and $\unicode[STIX]{x1D706}_{y}$ decreased under negative $u_{l}$ 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 $\langle -w\unicode[STIX]{x1D714}_{y}\rangle$ , 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 $\langle -w\unicode[STIX]{x1D714}_{y}\rangle$ 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 $\unicode[STIX]{x1D706}_{y}$ 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.

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