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Decay of streaks and rolls in plane Couette-Poiseuille flow. (English) Zbl 07333070
Summary: We report the results of an experimental investigation into the decay of turbulence in plane Couette-Poiseuille flow using ‘quench’ experiments where the flow laminarises after a sudden reduction in Reynolds number \(Re\). Specifically, we study the velocity field in the streamwise-spanwise plane. We show that the spanwise velocity containing rolls decays faster than the streamwise velocity, which displays elongated regions of higher or lower velocity called streaks. At final Reynolds numbers above \(425\), the decay of streaks displays two stages: first a slow decay when rolls are present and secondly a more rapid decay of streaks alone. The difference in behaviour results from the regeneration of streaks by rolls, called the lift-up effect. We define the turbulent fraction as the portion of the flow containing turbulence and this is estimated by thresholding the spanwise velocity component. It decreases linearly with time in the whole range of final \(Re\). The corresponding decay slope increases linearly with final \(Re\). The extrapolated value at which this decay slope vanishes is \(Re_{a_z}\approx 656\pm 10\), close to \(Re_g\approx 670\) at which turbulence is self-sustained. The decay of the energy computed from the spanwise velocity component is found to be exponential. The corresponding decay rate increases linearly with \(Re\), with an extrapolated vanishing value at \(Re_{A_z}\approx 688\pm 10\). This value is also close to the value at which the turbulence is self-sustained, showing that valuable information on the transition can be obtained over a wide range of \(Re\).
MSC:
76 Fluid mechanics
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[1] Agez, G., Clerc, M.G., Louvergneaux, E. & Rojas, R.G.2013Bifurcations of emerging patterns in the presence of additive noise. Phys. Rev. E87, 042919.
[2] Barkley, D. & Tuckerman, L.S.2005Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett.94, 014502. · Zbl 1124.76018
[3] Batchelor, G.K. & Townsend, A.A.1948Decay of turbulence in the final period. Proc. R. Soc. Lond. A194, 527-543. · Zbl 0032.22602
[4] Bottin, S. & Chaté, H.1998Statistical analysis of the transition to turbulence in plane Couette flow. Eur. Phys. J. B6, 143-155.
[5] Chantry, M., Tuckerman, L.S. & Barkley, D.2017Universal continuous transition to turbulence in a planar shear flow. J. Fluid Mech.824, R1.
[6] Couliou, M. & Monchaux, R.2015Large-scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism. Phys. Fluids27, 034101. · Zbl 1383.76188
[7] Daviaud, F., Hegseth, J. & Bergé, P.1992Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett.69, 2511-2514.
[8] De Souza, D., Bergier, T. & Monchaux, R.2020Transient states in plane Couette flow. J. Fluid Mech.903, A33.
[9] Duguet, Y., Schlartter, P. & Henningson, D.S.2010Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech.650, 119-129. · Zbl 1189.76254
[10] Duguet, Y. & Schlatter, P.2013Oblique laminar-turbulent interfaces in plane shear flows. Phys. Rev. Lett.110, 034502.
[11] Duriez, T., Aider, J.-L. & Wesfreid, J.E.2009Self-sustaining process through streak generation in a flat-plate boundary layer. Phys. Rev. Lett.103, 144502.
[12] Fransson, J.H.M., Matsubara, M. & Alfredsson, P.H.2005Transition induced by free-stream turbulence. J. Fluid Mech.527, 1-25. · Zbl 1142.76303
[13] García-Ojalvo, J. & Sancho, J.M.1999Noise in Spatially Extended Systems. Springer. · Zbl 0938.60002
[14] Gomé, S., Tuckerman, L.S. & Barkley, D.2020Statistical transition to turbulence in plane channel flow. Phys. Rev. Fluids5, 083905.
[15] Grebogi, C., Ott, E. & Yorke, J.A.1986Critical exponent of chaotic transients in nonlinear dynamical systems. Phys. Rev. Lett.57, 1284-1287.
[16] Hamilton, J.M., Kim, J. & Waleffe, F.1995Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech.287, 317-348. · Zbl 0867.76032
[17] Jiménez, J. & Moin, P.1991The minimal flow unit in near-wall turbulence. J. Fluid Mech.225, 213-240. · Zbl 0721.76040
[18] Klotz, L., Lemoult, G., Frontczak, I., Tuckerman, L.S. & Wesfreid, J.E.2017Couette-Poiseuille flow experiment with zero mean advection velocity: subcritical transition to turbulence. Phys. Rev. Fluids2, 043904.
[19] Klotz, L., Pavlenko, A. & Wesfreid, J.E.2021Experimental measurements in plane Couette-Poiseuille flow: Dynamics of the large- and small-scale flow. J. Fluid Mech.912, A24. · Zbl 07315236
[20] Klotz, L. & Wesfreid, J.E.2017Experiments on transient growth of turbulent spots. J. Fluid Mech.829, R4. · Zbl 07136098
[21] Kreilos, T., Khapko, T., Schlatter, P., Duguet, Y., Henningson, D.S. & Eckhardt, B.2016Bypass transition and spot nucleation in boundary layers. Phys. Rev. Fluids1, 043602. · Zbl 1284.76106
[22] Le Gal, P., Tasaka, Y., Cros, A. & Yamaguchi, K.2007A statistical study of spots in torsional Couette flow. J. Engng Maths57, 289-302. · Zbl 1192.76064
[23] Lemoult, G., Aider, J.-L. & Wesfreid, J.E.2013Turbulent spots in a channel: large-scale flow and self-sustainability. J. Fluid Mech.731, R1. · Zbl 1294.76165
[24] Orszag, S.A.1971Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech.50, 689-703. · Zbl 0237.76027
[25] Paranjape, C.S.2019 Onset of turbulence in plane poiseuille flow. PhD thesis, Institute of Science and Technology Austria.
[26] Peixinho, J. & Mullin, T.2006Decay of turbulence in pipe flow. Phys. Rev. Lett.96, 094501. · Zbl 1114.76304
[27] Philip, J. & Manneville, P.2011From temporal to spatiotemporal dynamics in transitional plane Couette flow. Phys. Rev. E83, 036308.
[28] Prigent, A.2001 La spirale turbulente : motif de grande longueur d’onde dans les écoulements cisaillés turbulents. PhD thesis, Université Paris XI.
[29] Prigent, A. & Dauchot, O.2005 Transition to versus from turbulence in sub-critical Couette flows. In IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions (ed. T. Mullin & R. Kerswell). Springer.
[30] Puckert, D.K., Dieterle, M. & Rist, U.2017Reduction of freestream turbulence at low velocities. Exp. Fluids58, 45.
[31] Rolland, J.2015Mechanical and statistical study of the laminar hole formation in transitional plane Couette flow. Eur. Phys. J. B88 (3), 66.
[32] Rolland, J.2018aExtremely rare collapse and build-up of turbulence in stochastic models of transitional wall flows. Phys. Rev. E97, 023109.
[33] Rolland, J.2018bFinite size analysis of a double crossover in transitional wall turbulence. J. Stat. Mech.2018 (9), 093207. · Zbl 1456.76058
[34] Rolland, J. & Manneville, P.2011Ginzburg-Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow. Eur. J. Phys. B80, 529-544.
[35] Sano, M. & Tamai, K.2016A universal transition to turbulence in channel flow. Nat. Phys.12, 249-253.
[36] Schmid, P.J. & Henningson, D.S.2001Stability and Transition in Shear Flows. Springer.
[37] Schneider, T.M., De Lillo, F., Buehrle, J., Eckhardt, B., Dörnemann, T., Dörnemann, K. & Freisleben, B.2010Transient turbulence in plane Couette flow. Phys. Rev. E81, 015301.
[38] Seki, D. & Matsubara, M.2012Experimental investigation of relaminarizing and transitional channel flows. Phys. Fluids24 (12), 124102.
[39] Shi, L., Avila, M. & Hof, B.2013Scale invariance at the onset of turbulence in Couette flow. Phys. Rev. Lett.110, 204502.
[40] Shimizu, M. & Manneville, P.2019Bifurcations to turbulence in transitional channel flow. Phys. Rev. Fluids4, 113903.
[41] Tillmark, N. & Alfredsson, P.H.1992Experiments on transition in plane Couette flow. J. Fluid Mech.235, 89-102.
[42] Tsanis, I.K. & Leutheusser, H.J.1988The structure of turbulent shear-induced countercurrent flow. J. Fluid Mech.189, 531-552.
[43] Waleffe, F.1997On a self-sustaining process in shear flows. Phys. Fluids9 (4), 883-900.
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