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Growth dynamics of turbulent spots in plane Couette flow. (English) Zbl 1383.76188
Summary: We experimentally and numerically investigate the temporal aspects of turbulent spots spreading in a plane Couette flow for transitional Reynolds numbers between 300 and 450. Spot growth rate, spot advection rate and large-scale flow intensity are measured as a function of time and Reynolds number. All these quantities show similar dynamics clarifying the role played by large-scale flows in the advection of the turbulent spot. The contributions of each possible growth mechanism, that is, growth induced by large-scale advection or growth by destabilization, are discussed for the different stages of the spot growth. A scenario that gathers all these elements is providing a better understanding of the growth dynamics of turbulent spots in plane Couette flow that should possibly apply to other extended shear flows.

MSC:
76F06 Transition to turbulence
76Exx Hydrodynamic stability
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
Software:
channelflow
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[1] Barkley, D.; Song, B.; Mukund, V.; Lemoult, G.; Avila, M.; Hof, B., The rise of fully turbulent flow, Nature, 526, 550-553, (2015)
[2] Barkley, D.; Tuckerman, L. S., Computational study of turbulent – laminar patterns in Couette flow, Phys. Rev. Lett., 94, (2005)
[3] Barkley, D.; Tuckerman, L. S., Mean flow of turbulent – laminar patterns in plane Couette flow, J. Fluid Mech., 576, 109-137, (2007) · Zbl 1124.76018
[4] Bottin, S.; Dauchot, O.; Daviaud, F., Intermittency in a locally forced plane Couette flow, Phys. Rev. Lett., 79, 4377, (1997)
[5] Bottin, S.; Dauchot, O.; Daviaud, F.; Manneville, P., Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow, Phys. Fluids, 10, 2597-2607, (1998)
[6] Chantry, M.; Tuckerman, L. S.; Barkley, D., Turbulent – laminar patterns in shear flows without walls, J. Fluid Mech., 791, R8, (2016) · Zbl 1382.76106
[7] Coles, D., Transition in circular Couette flow, J. Fluid Mech., 21, 385-425, (1965) · Zbl 0134.21705
[8] Couliou, M.; Monchaux, R., Large scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism, Phys. Fluids, 27, (2015)
[9] Couliou, M.; Monchaux, R., Spreading of turbulence in plane Couette flow, Phys. Rev. E, 93, (2016)
[10] Dauchot, O.; Daviaud, F., Finite amplitude perturbation and spots growth mechanism in plane Couette flow, Phys. Fluids, 7, 335-343, (1995)
[11] Duguet, Y.; Le Maître, O.; Schlatter, P., Stochastic and deterministic motion of a laminar – turbulent front in a spanwisely extended Couette flow, Phys. Rev. E, 84, (2011)
[12] Duguet, Y.; Schlatter, P., Oblique laminar – turbulent interfaces in plane shear flows, Phys. Rev. Lett., 110, (2013)
[13] Duguet, Y.; Schlatter, P.; Henningson, D. S., Formation of turbulent patterns near the onset of transition in plane Couette flow, J. Fluid Mech., 650, 119-129, (2010) · Zbl 1189.76254
[14] Emmons, H. W., The laminar – turbulent transition in a boundary layer. Part 1, J. Aerosp. Sci., 18, 490-498, (1951) · Zbl 0043.19109
[15] Gad-El-Hak, M.; Blackwelderf, R. F.; Riley, J., On the growth of turbulent regions in laminar boundary layers, J. Fluid Mech., 110, 73-95, (1981)
[16] Gibson, J. F.2014 Channelflow: a spectral Navier-Stokes simulator in \(\text{C}^{++}\). Tech. Rep. University of New Hampshire; Channelflow.org.
[17] Gibson, J. F.; Halcrow, J.; Cvitanović, P., Visualizing the geometry of state space in plane Couette flow, J. Fluid Mech., 611, 107-130, (2008) · Zbl 1151.76453
[18] Hashimoto, S., Hasobe, A., Tsukahara, T., Kawaguchi, Y. & Kawamura, H.2009An experimental study on turbulent-stripe structure in transitional channel flow. In Proceedings of the Sixth International Symposium on Turbulence, Heat and Mass Transfer (ed. Hanjalić, K., Nagano, Y. & Jakirlić, S.), pp. 193-196. Begell House.
[19] Hegseth, J. J., Turbulent spots in plane Couette flow, Phys. Rev. E, 54, 4915-4923, (1996)
[20] Henningson, D. S.; Alfredsson, P. H., The wave structure of turbulent spots in plane Poiseuille flow, J. Fluid Mech., 178, 405-421, (1987)
[21] Henningson, D. S.; Johansson, A. V.; Alfredsson, P. H., Turbulent spots in channel flows, J. Engng Maths, 28, 21-42, (1994) · Zbl 0793.76047
[22] Lagha, M.; Manneville, P., Modeling of plane Couette flow. I. Large scale flow around turbulent spots, Phys. Fluids, 19, (2007) · Zbl 1182.76422
[23] Lemoult, G.; Aider, J.-L.; Wesfreid, J. E., Turbulent spots in a channel: large-scale flow and self-sustainability, J. Fluid Mech., 731, R1, (2013) · Zbl 1294.76165
[24] Lundbladh, A.; Johansson, A. V., Direct simulation of turbulent spots in plane Couette flow, J. Fluid Mech., 229, 499-516, (1991) · Zbl 0850.76256
[25] Manneville, P.2015 Towards a model of large scale dynamics in transitional wall-bounded flows, arXiv:1504.00664.
[26] Philip, J.; Manneville, P., From temporal to spatiotemporal dynamics in transitional plane Couette flow, Phys. Rev. E, 83, (2011)
[27] Prigent, A. & Dauchot, O.2005Transition to versus from turbulence in subcritical Couette flows. In IUATM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions, pp. 195-219. Springer. doi:10.1007/1-4020-4049-0_11
[28] Prigent, A.; Grégoire, G.; Chaté, H.; Dauchot, O.; Van Saarloos, W., Large-scale finite-wavelength modulation within turbulent shear flows, Phys. Rev. Lett., 89, (2002)
[29] Schumacher, J.; Eckhardt, B., Evolution of turbulent spots in a parallel shear flow, Phys. Rev. E, 63, (2001)
[30] Tillmark, N., On the spreading mechanisms of a turbulent spot in plane Couette flow, Eur. Phys. Lett., 32, 481-485, (1995)
[31] Tillmark, N.; Alfredsson, P. H., Experiments on transition in plane Couette flow, J. Fluid Mech., 235, 89-102, (1992)
[32] Tuckerman, L. S.; Barkley, D.; Dauchot, O., Statistical analysis of the transition to turbulent – laminar banded patterns in plane Couette flow, J. Phys.: Conf. Ser., 137, (2008)
[33] Tuckerman, L. S.; Kreilos, T.; Schrobsdorff, H.; Schneider, T. M.; Gibson, J. F., Turbulent – laminar patterns in plane Poiseuille flow, Phys. Fluids, 26, (2014)
[34] Van Atta, C., Exploratory measurements in spiral turbulence, J. Fluid Mech., 25, 495-512, (1966)
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