Abstract
This study is motivated by the observation that the drag-reduction effectiveness achieved by the imposition of oscillatory spanwise wall motion declines with Reynolds number. The question thus posed is whether the decline is linked to the increasingly strong influence of large-scale outer structures in the log layer on the near-wall turbulence, in general, and the streak strength in the viscosity-affected layer, in particular – a process referred to as modulation. This question is addressed via an extensive statistical analysis of DNS data for a channel flow at a friction Reynolds number 1020, subjected to oscillatory spanwise wall motion at a nominal wall-scaled period of 100. The analysis rests on a separation of turbulent scales by means of the Empirical Mode Decomposition. This method is used to derive conditional statistics of small-scale motions and skin friction subject to prescribed intensity of large-scale motions – referred to as footprinting. It is shown that the large-scale fluctuations are responsible, directly on their own, for roughly 30% to the skin friction. Positive large-scale fluctuations are also shown to be the cause of a major amplification of small-scale streaks, relative to weak attenuation by negative fluctuations. This highly asymmetric process is likely to be indirectly influential on the drag-reduction process, although it is not possible to identify this indirect effect in quantitative terms as part of the present analysis.
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Agostini, L., Touber, E., Leschziner, M.A.: Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at. J. Fluid Mech. 743, 606–635 (2014)
Agostini, L., Touber, E., Leschziner, M.: The turbulence vorticity as a window to the physics of friction-drag reduction by oscillatory wall motion. Int. J. Heat Fluid Flow 51, 3–15 (2015)
Chung, Y.M., Hurst, E., Yang, Q. Zhou, Y., Lucey, A., Liu, Y., Huang, L. (eds.): DNS for turbulent drag reduction at R e τ = 1600. Springer, Berlin (2016)
Gatti, D., Quadrio, M.: Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number. Phys. Fluids 25(12), 125109 (2013)
Quadrio, M., Ricco, P.: Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521, 251–271 (2004)
Quadrio, M., Ricco, P., Viotti, C.: Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178 (2009)
Touber, E., Leschziner, M.A.: Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 693, 150–200 (2012)
Viotti, C., Quadrio, M., Luchini, P.: Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction. Phys. fluids 21(11), 115109 (2009)
Lardeau, S., Leschziner, M.A.: The streamwise drag-reduction response of a boundary layer subjected to a sudden imposition of transverse oscillatory wall motion. Phys. Fluids 25(7), 075109 (2013)
Ricco, P.: Modification of near-wall turbulence due to spanwise wall oscillations. J. Turbul. 5, 20–20 (2004)
Skote, M.: Turbulent boundary layer flow subject to streamwise oscillation of spanwise wall-velocity. Phys. Fluids 23(8), 081703 (2011)
Skote, M.: Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall. Int. J. Heat Fluid Flow 38, 1–12 (2012)
Skote, M.: Comparison between spatial and temporal wall oscillations in turbulent boundary layer flows. J. Fluid Mech. 730, 273–294 (2013)
Yudhistira, I., Skote, M.: Direct numerical simulation of a turbulent boundary layer over an oscillating wall. J. Turbul. 12, N9 (2011)
Hurst, E., Yang, Q., Chung, Y.M.: The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves. J. Fluid Mech. 759, 28–55 (2014)
Gatti, D., Quadrio, M.: Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing. J. Fluid Mech. 802, 553–582 (2016)
Luchini, P.: Reducing the turbulent skin friction. In: Desideri, J.-A., et al (eds.) Proc. 3rd ECCOMAS CFD conference on computational methods in applied sciences 1996, pp 466–470. Wiley (1996)
Mathis, R., Hutchins, N., Marusic, I.: Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337 (2009)
Hutchins, N., Monty, J.P., Ganapathisubramani, B., Ng, H.C.H., Marusic, I.: Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 673, 255–285 (2011)
Hutchins, N., Nickels, T.B., Marusic, I., Chong, M.: Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136 (2009)
Marusic, I., Mathis, R., Hutchins, N.: Predictive model for wall-bounded turbulent flow. Science 329(5988), 193–196 (2010)
Mathis, R., Monty, J.P., Hutchins, N., Marusic, I.: Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows. Phys. Fluids 21(11), 111703 (2009)
Agostini, L., Leschziner, M., Gaitonde, D.: Skewness-induced asymmetric modulation of small-scale turbulence by large-scale structures. Phys. Fluids 28(1), 015110 (2016)
Bernardini, M., Pirozzoli, S.: Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys. Fluids 23(6), 061701 (2011)
Schlatter, P., Örlü, R.: Quantifying the interaction between large and small scales in wall-bounded turbulent flows: A note of caution. Phys. Fluids 22(5), 051704 (2010)
Zhang, C., Chernyshenko, S.I.: Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence. Physical Review Fluids 1(1), 014401 (2016)
Agostini, L., Leschziner, M.: On the validity of the quasi-steady-turbulence hypothesis in representing the effects of large scales on small scales in boundary layers. Phys. Fluids 28(4), 045102 (2016)
Agostini, L., Leschziner, M.: Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28(1), 015107 (2016)
de Giovanetti, M., Hwang, Y., Choi, H.: Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech. 808, 511–538 (2016)
Agostini, L., Leschziner, M.: On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26(7), 075107 (2014)
Blesbois, O., Chernyshenko, S.I., Touber, E., Leschziner, M.A.: Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation. J. Fluid Mech. 724, 607–641 (2013)
Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to R e τ = 590. Phys. Fluids 11(4), 943–945 (1999)
Lozano-Durán, A., Jiménez, J.: Effect of the computational domain on direct simulations of turbulent channels up to R e τ = 4200. Phys. Fluids 26(1), 011702 (2014)
Lee, M., Moser, R.D.: Direct numerical simulation of turbulent channel flow up to R e τ = 5200. J. Fluid Mech. 774, 395–415 (2015)
Agostini, L., Leschziner, M.: Spectral analysis of near-wall turbulence in channel flow at R e τ = 4200 with emphasis on the attached-eddy hypothesis. Physical Review Fluids 2(1), 014603 (2017)
Hoyas, S., Jiménez, J.: Scaling of the velocity fluctuations in turbulent channels up to R e τ = 2003. Phys. Fluids 8(1), 011702 (2006)
Jiménez, J.: Near-wall turbulence. Phys. Fluids 25(10), 101302 (2013)
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Phys. Eng. Sci. 454(1971), 903–995 (1998)
Flandrin, P., Rilling, G., Goncalves, P.: Empirical mode decomposition as a filter bank. IEEE Signal Process Lett. 11(2), 112–114 (2004)
Wu, Z., Huang, N.: A study of the characteristics of white noise using the empirical mode decomposition method. In: Proceedings of the royal society of London a: mathematical, physical and engineering sciences. The Royal Society 460, 1597–1611 (2004)
Townsend, A.A.: The structure of turbulent shear flow. Cambridge University press, Cambridge (1980)
Perry, A., Chong, M.: On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217 (1982)
Davidson, P., Krogstad, P.A., Nickels, T., et al.: A refined interpretation of the logarithmic structure function law in wall layer turbulence. Phys. Fluids 18(6), 065112 (2006)
Lozano-Durán, A., Jiménez, J.: Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471 (2014)
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The research reported in this paper was undertaken within the framework of the EU-China project DRAGY, Grant Agreement 690623.
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Agostini, L., Leschziner, M. The Impact of Footprints of Large-Scale Outer Structures on the Near-Wall Layer in the Presence of Drag-Reducing Spanwise Wall Motion. Flow Turbulence Combust 100, 1037–1061 (2018). https://doi.org/10.1007/s10494-018-9917-3
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DOI: https://doi.org/10.1007/s10494-018-9917-3