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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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Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Re 𝜏 = 640. Trans. ASME J. Fluids Engng 126 (5), 835843.
Adrian, R. J., Christensen, K. T. & Liu, Z. C. 2000 Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275290.
Agostini, L. & Leschziner, M. A. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.
Ahn, J., Lee, J. H., Jang, S. J. & Sung, H. J. 2013 Direct numerical simulations of fully developed turbulent pipe flows for Re 𝜏 = 180, 544 and 934. Intl J. Heat Fluid Flow 44, 222228.
Ahn, J., Lee, J. H., Lee, J., Kang, J.-H & Sung, H. J. 2015 Direct numerical simulation of a 30R long turbulent pipe flow at Re 𝜏 = 3008. Phys. Fluids 27 (6), 065110.
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41.
Balakumar, B. J. & Adrian, R. J. 2007 Large-and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365 (1852), 665681.
Bandyopadhyay, P. R. & Hussain, A. K. M. F. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 22212228.
Bernardini, M. & Pirozzoli, S. 2011 Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys. Fluids 23 (6), 061701.
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243S252.
Chauhan, K. A., Monkewitz, P. A. & Nagib, H. M. 2009 Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn. Res. 41 (2), 021404.
Chernyshenko, S. I., Marusic, I. & Mathis, R.2012 Quasi-steady description of modulation effects in wall turbulence. arXiv:1203.3714.
Chin, C., Philip, J., Klewicki, J., Ooi, A. & Marusic, I. 2014 Reynolds-number-dependent turbulent inertia and onset of log region in pipe flows. J. Fluid Mech. 757, 747769.
Chung, D. & McKeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341364.
Chung, D., Monty, J. P. & Ooi, A. 2014 An idealised assessment of Townsend’s outer-layer similarly hypothesis for wall turbulence. J. Fluid Mech. 742, R3.
Dennis, D. J. C. & Nickels, T. B. 2011 Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures. J. Fluid Mech. 673, 218244.
Fiscaletti, D., Ganapathisubramani, B. & Elsinga, G. E. 2015 Amplitude and frequency modulation of the small scales in a jet. J. Fluid Mech. 772, 756783.
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), 1317.
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 6191.
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 3546.
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.
Guala, M., Metzger, M. & McKeon, B. J. 2011 Interactions within the turbulent boundary layer at high Reynolds number. J. Fluid Mech. 666, 573604.
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647664.
Hutchins, N., Monty, J. P., Ganapathisubramani, B., Ng, H. C. H. & Marusic, I. 2011 Three-dimensional conditional structure of a high Reynolds number turbulent boundary layer. J. Fluid Mech. 673, 255285.
Hwang, J., Lee, J. & Sung, H. J. 2016a Influence of large-scale accelerating motions on turbulent pipe and channel flows. J. Fluid Mech. 804, 420441.
Hwang, J., Lee, J., Sung, H. J. & Zaki, T. A. 2016b Inner-outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128157.
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185212.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185214.
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.
Kim, K., Baek, S. J. & Sung, H. J. 2002 An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38 (2), 125138.
Lee, J. H. & Sung, H. J. 2011 Very-large-scale motions in a turbulent boundary layer. J. Fluid Mech. 673, 80120.
Lee, J. H. & Sung, H. J. 2013 Comparison of very-large-scale motions of turbulent pipe and boundary layer simulations. Phys. Fluids 25 (4), 045103.
Liu, Z., Adrian, R. J. & Hanratty, T. J. 2001 Large-scale modes of turbulent channel flow: transport and structure. J. Fluid Mech. 448, 5380.
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193196.
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311337.
Mathis, R., Marusic, I., Chernyshenko, S. L. & Hutchins, N. 2013 Estimating wall-shear-stress fluctuations given an outer region input. J. Fluid Mech. 715, 163180.
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.
Örlü, R. & Schlatter, P. 2011 On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows. Phys. Fluids 23, 021704.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601639.
Schlatter, P. & Örlü, R. 2010a Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116126.
Schlatter, P. & Örlü, R. 2010b Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution. Phys. Fluids 22 (5), 051704.
Schlatter, P., Örlü, R., Li, Q., Brethouwer, G., Fransson, J. H., Johansson, A. V., Alfredsson, P. H. & Henningson, D. S. 2009 Turbulent boundary layers up to Re 𝜃 = 2500 studied through simulation and experiment. Phys. Fluids 21 (5), 51702.
Smits, A. J., Matheson, N. & Joubert, P. N. 1983 Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients. J. Ship Res. 27, 147157.
Talluru, K. M., Baidya, R., Hutchins, N. & Marusic, I. 2014 Amplitude modulation of all three velocity components in turbulent boundary layers. J. Fluid Mech. 746, R1.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Toh, S. & Itano, T. 2005 Interaction between a large-scale structure and near-wall structures in channel flow. J. Fluid Mech. 524, 249262.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Wu, X., Baltzer, J. R. & Adrian, R. J. 2012 Direct numerical simulation of a 30R long turbulent pipe flow at R + = 685: large- and very large-scale motions. J. Fluid Mech. 698, 235281.
Yoon, M., Ahn, J., Hwang, J. & Sung, H. J. 2016a Contribution of velocity–vorticity correlations to the frictional drag in wall-bounded turbulent flows. Phys. Fluids 28 (8), 081702.
Yoon, M., Hwang, J., Lee, J., Sung, H. J. & Kim, J. 2016b Large-scale motions in a turbulent channel flow with the slip boundary condition. Intl J. Heat Fluid Flow 61, 96107.
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.
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