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Turbulence collapse in a suction boundary layer. (English) Zbl 1359.76144
Summary: Turbulence in the asymptotic suction boundary layer is investigated numerically at the verge of laminarisation using direct numerical simulation. Following an adiabatic protocol, the Reynolds number \(Re\) is decreased in small steps starting from a fully turbulent state until laminarisation is observed. Computations in a large numerical domain allow in principle for the possible coexistence of laminar and turbulent regions. However, contrary to other subcritical shear flows, no laminar-turbulent coexistence is observed, even near the onset of sustained turbulence. High-resolution computations suggest a critical Reynolds number \(Re_{g}\approx 270\), below which turbulence collapses, based on observation times of \(O(10^{5})\) inertial time units. During the laminarisation process, the turbulent flow fragments into a series of transient streamwise-elongated structures, whose interfaces do not display the characteristic obliqueness of classical laminar-turbulent patterns. The law of the wall, i.e. logarithmic scaling of the velocity profile, is retained down to \(Re_{g}\), suggesting a large-scale wall-normal transport absent in internal shear flows close to the onset. In order to test the effect of these large-scale structures on the near-wall region, an artificial volume force is added to damp spanwise and wall-normal fluctuations above \(y^{+}=100\), in viscous units. Once the largest eddies have been suppressed by the forcing, and thus turbulence is confined to the near-wall region, oblique laminar-turbulent interfaces do emerge as in other wall-bounded flows, however only transiently. These results suggest that oblique stripes at the onset are a prevalent feature of internal shear flows, but will not occur in canonical boundary layers, including the spatially growing ones.

76F40 Turbulent boundary layers
76F06 Transition to turbulence
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[1] Alfredsson, P. H. & Matsubara, M.2000 Free-stream turbulence, streaky structures and transition in boundary layer flows AIAA Paper 2534.
[2] Ansorge, C.; Mellado, J. P., Global intermittency and collapsing turbulence in the stratified planetary boundary layer, Boundary-Layer Meteorol., 153, 89-116, (2014)
[3] Antonia, R. A.; Fulachier, L.; Krishnamoorthy, L. V.; Benabid, T.; Anselmet, F., Influence of wall suction on the organized motion in a turbulent boundary layer, J. Fluid Mech., 190, 217-240, (1988)
[4] Avila, K.; Moxey, D.; De Lozar, A.; Avila, M.; Barkley, D.; Hof, B., The onset of turbulence in pipe flow, Science, 333, 6039, 192-196, (2011) · Zbl 1411.76035
[5] Barkley, D.; Tuckerman, L. S., Computational study of turbulent laminar patterns in Couette flow, Phys. Rev. Lett., 94, (2005)
[6] Bobke, A.; Örlü, R.; Schlatter, P., Simulations of turbulent asymptotic suction boundary layers, J. Turbul., 17, 155-178, (2015)
[7] Bottin, S.; Daviaud, F.; Manneville, P.; Dauchot, O., Discontinuous transition to spatiotemporal intermittency in plane Couette flow, Europhys. Lett., 43, 2, 171-176, (1998)
[8] Brethouwer, G.; Duguet, Y.; Schlatter, P., Turbulent – laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces, J. Fluid Mech., 704, 137-172, (2012) · Zbl 1246.76028
[9] Chaté, H. & Manneville, P.1994Spatiotemporal intermittency. In Turbulence (ed. Tabeling, P. & Cardoso, O.), , vol. 341, pp. 111-116. Springer. doi:10.1007/978-1-4615-2586-8_19
[10] Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S.2007 A pseudo-spectral solver for incompressible boundary layer flows, Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden.
[11] Ching, C. Y., Djenidi, L. & Antonia, R. A.1996Low Reynolds number effects on the inner region of a turbulent boundary layer. In Developments in Laser Techniques and Applications to Fluid Mechanics (ed. Adrian, R. J., Durão, D. F. G., Durst, F., Heitor, M. V., Maeda, M. & Whitelaw, J. H.), pp. 3-15. Springer. doi:10.1007/978-3-642-79965-5_1
[12] Coles, D., Transition in circular Couette flow, J. Fluid Mech., 21, 3, 385-425, (1965) · Zbl 0134.21705
[13] Cros, A.; Le Gal, P., Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk, Phys. Fluids, 14, 11, 3755-3765, (2002) · Zbl 1185.76095
[14] Deusebio, E.; Brethouwer, G.; Schlatter, P.; Lindborg, E., A numerical study of the unstratified and stratified Ekman layer, J. Fluid Mech., 755, 672-704, (2014)
[15] Duguet, Y.; Schlatter, P., Oblique laminar – turbulent interfaces in plane shear flows, Phys. Rev. Lett., 110, (2013)
[16] 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
[17] Emmons, H. W., The laminar – turbulent transition in a boundary layer - Part I, J. Aero. Sci., 18, 7, 490-498, (1951) · Zbl 0043.19109
[18] Fransson, J. H. M.; Alfredsson, P. H., On the disturbance growth in an asymptotic suction boundary layer, J. Fluid Mech., 482, 51-90, (2003) · Zbl 1049.76508
[19] Hall, P.; Smith, F. T., On strongly nonlinear vortex/wave interactions in boundary-layer transition, J. Fluid Mech., 227, 641-666, (1991) · Zbl 0721.76027
[20] Hamilton, J. M.; Kim, J.; Waleffe, F., Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech., 287, 317-348, (1995) · Zbl 0867.76032
[21] Hegseth, J. J.; Andereck, C. D.; Hayot, F.; Pomeau, Y., Spiral turbulence and phase dynamics, Phys. Rev. Lett., 62, 3, 257-260, (1989)
[22] Henningson, D. S.; Spalart, P. R.; Kim, J., Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow, Phys. Fluids, 30, 10, 2914-2917, (1987)
[23] Hocking, L. M., Non-linear instability of the asymptotic suction velocity profile, Q. J. Mech. Appl. Maths, 28, 3, 341-353, (1975) · Zbl 0321.76021
[24] Jeong, J.; Hussain, F., On the identification of a vortex, J. Fluid Mech., 285, 69-94, (1995) · Zbl 0847.76007
[25] Jiménez, J., The largest scales of turbulent wall flows, CTR Annu. Res. Briefs, 137-154, (1998)
[26] Jiménez, J.; Moin, P., The minimal flow unit in near-wall turbulence, J. Fluid Mech., 225, 213-240, (1991) · Zbl 0721.76040
[27] Jiménez, J.; Pinelli, A., The autonomous cycle of near-wall turbulence, J. Fluid Mech., 389, 335-359, (1999) · Zbl 0948.76025
[28] Kametani, Y.; Fukagata, K.; Örlü, R.; Schlatter, P., Effect of uniform blowing/suction in a turbulent boundary layer at moderate Reynolds number, Intl J. Heat Fluid Flow, 55, 132-142, (2015)
[29] Khapko, T.2014 Transition to turbulence in the asymptotic suction boundary layer. Licentiate Thesis, KTH Mechanics, Stockholm.
[30] Khapko, T.; Duguet, Y.; Kreilos, T.; Schlatter, P.; Eckhardt, B.; Henningson, D. S., Complexity of localised coherent structures in a boundary-layer flow, Eur. Phys. J. E, 37, 4, 32, (2014) · Zbl 1284.76106
[31] Khapko, T.; Kreilos, T.; Schlatter, P.; Duguet, Y.; Eckhardt, B.; Henningson, D. S., Localised edge states in the asymptotic suction boundary layer, J. Fluid Mech., 717, R6, (2013) · Zbl 1284.76106
[32] Kreilos, T., Khapko, T., Schlatter, P., Duguet, Y., Henningson, D. S. & Eckhardt, B.2016Bypass transition and spot nucleation in boundary layers. Phys. Rev. Fluids (submitted). · Zbl 1284.76106
[33] Kreilos, T.; Veble, G.; Schneider, T. M.; Eckhardt, B., Edge states for the turbulence transition in the asymptotic suction boundary layer, J. Fluid Mech., 726, 100-122, (2013) · Zbl 1287.76122
[34] Lemoult, G.; Shi, L.; Avila, K.; Jalikop, S. V.; Avila, M.; Hof, B., Directed percolation phase transition to sustained turbulence in Couette flow, Nat. Phys., 12, 254-258, (2016)
[35] Levin, O.; Henningson, D. S., Turbulent spots in the asymptotic suction boundary layer, J. Fluid Mech., 584, 397-414, (2007) · Zbl 1123.76023
[36] Manneville, P., Spatiotemporal perspective on the decay of turbulence in wall-bounded flows, Phys. Rev. E, 79, (2009)
[37] Manneville, P., On the decay of turbulence in plane Couette flow, Fluid Dyn. Res., 43, (2011) · Zbl 1421.76108
[38] Manneville, P.; Rolland, J., On modelling transitional turbulent flows using under-resolved direct numerical simulations: the case of plane Couette flow, Theor. Comput. Fluid Dyn., 25, 407-420, (2011) · Zbl 1272.76140
[39] Mariani, P., Spalart, P. R. & Kollmann, W.1993Direct simulation of a turbulent boundary layer with suction. In Near-Wall Turbulent Flows (ed. So, R. M. C., Speziale, C. G. & Launder, B. E.), pp. 347-356. Elsevier Science.
[40] Marusic, I.; Mathis, R.; Hutchins, N., Predictive model for wall-bounded turbulent flow, Science, 329, 193-196, (2010) · Zbl 1226.76015
[41] 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) · Zbl 1181.76008
[42] Moxey, D.; Barkley, D., Distinct large-scale turbulent-laminar states in transitional pipe flow, Proc. Natl Acad. Sci. USA, 107, 18, 8091-8096, (2010)
[43] Orlandi, P.; Bernardini, M.; Pirozzoli, S., Poiseuille and Couette flows in the transitional and fully turbulent regime, J. Fluid Mech., 770, 424-441, (2015)
[44] Philip, J.; Manneville, P., From temporal to spatiotemporal dynamics in transitional plane Couette flow, Phys. Rev. E, 83, (2011)
[45] Prigent, A.2001 La spirale turbulente: motif de grande longueur d’onde dans les écoulements cisaillés turbulents. PhD thesis, Université Paris XI, Paris.
[46] Prigent, A.; Grégoire, G.; Chaté, H.; Dauchot, O.; Van Saarloos, W., Large-scale finite-wavelength modulation within turbulent shear flows, Phys. Rev. Lett., 89, 1, (2002)
[47] Reynolds, G. A.; Saric, W. S., Experiments on the stability of the flat-plate boundary layer with suction, AIAA J., 24, 2, 202-207, (1986)
[48] Sano, M.; Tamai, K., A universal transition to turbulence in channel flow, Nat. Phys., 12, 249-253, (2016)
[49] Schlatter, P.; Örlü, R., Assessment of direct numerical simulation data of turbulent boundary layers, J. Fluid Mech., 659, 116-126, (2010) · Zbl 1205.76139
[50] Schlatter, P.; Örlü, R., Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution, Phys. Fluids, 22, (2010) · Zbl 1190.76110
[51] Schlatter, P.; Örlü, R., Turbulent asymptotic suction boundary layers studied by simulation, J. Phys.: Conf. Ser., 318, (2011)
[52] Schlichting, H., Boundary-Layer Theory, (1987), McGraw-Hill
[53] Seki, D.; Matsubara, M., Experimental investigation of relaminarizing and transitional channel flows, Phys. Fluids, 24, (2012)
[54] Simpson, R. L.1967 The turbulent boundary layer on a porous plate: an experimental study of the fluid dynamics with injection and suction. PhD thesis, Department of Mechanical Engineering, Stanford University.
[55] Townsend, A. A., The Structure of Turbulent Shear Flow, (1956), Cambridge University Press · Zbl 0070.43002
[56] Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D.2005DNS of turbulent channel flow at very low Reynolds numbers. In Fourth International Symposium on Turbulence and Shear Flow Phenomena, pp. 935-940.
[57] Waleffe, F., On a self-sustaining process in shear flows, Phys. Fluids, 9, 4, 883-900, (1997)
[58] Willis, A. P.; Kerswell, R. R., Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized ‘edge’ states, J. Fluid Mech., 619, 213-233, (2009) · Zbl 1156.76395
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