Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T08:08:54.544Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence collapse in a suction boundary layer

Published online by Cambridge University Press:  14 April 2016

T. Khapko ,
P. Schlatter ,
Y. Duguet  and
D. S. Henningson
T. Khapko*
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Swedish e-Science Research Centre (SeRC), Sweden
P. Schlatter
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Swedish e-Science Research Centre (SeRC), Sweden
Y. Duguet
Affiliation:
LIMSI, CNRS, Université Paris-Saclay, F-91405 Orsay, France
D. S. Henningson
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Swedish e-Science Research Centre (SeRC), Sweden
*
†Email address for correspondence: taras@mech.kth.se
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent transition
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 356 - 379
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alfredsson, P. H. & Matsubara, M.2000 Free-stream turbulence, streaky structures and transition in boundary layer flows AIAA Paper 2534.Google Scholar
Ansorge, C. & Mellado, J. P. 2014 Global intermittency and collapsing turbulence in the stratified planetary boundary layer. Boundary-Layer Meteorol. 153, 89–116.Google Scholar
Antonia, R. A., Fulachier, L., Krishnamoorthy, L. V., Benabid, T. & Anselmet, F. 1988 Influence of wall suction on the organized motion in a turbulent boundary layer. J. Fluid Mech. 190, 217–240.CrossRefGoogle Scholar
Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D. & Hof, B. 2011 The onset of turbulence in pipe flow. Science 333 (6039), 192–196.Google Scholar
Barkley, D. & Tuckerman, L. S. 2005 Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett. 94, 014502.Google Scholar
Bobke, A., Örlü, R. & Schlatter, P. 2015 Simulations of turbulent asymptotic suction boundary layers. J. Turbul. 17, 155–178.Google Scholar
Bottin, S., Daviaud, F., Manneville, P. & Dauchot, O. 1998 Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhys. Lett. 43 (2), 171–176.Google Scholar
Brethouwer, G., Duguet, Y. & Schlatter, P. 2012 Turbulent–laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces. J. Fluid Mech. 704, 137–172.Google Scholar
Chaté, H. & Manneville, P. 1994 Spatiotemporal intermittency. In Turbulence (ed. Tabeling, P. & Cardoso, O.), NATO ASI Series, vol. 341, pp. 111–116. Springer.Google Scholar
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.Google Scholar
Ching, C. Y., Djenidi, L. & Antonia, R. A. 1996 Low 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.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21 (3), 385–425.Google Scholar
Cros, A. & Le Gal, P. 2002 Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk. Phys. Fluids 14 (11), 3755–3765.Google Scholar
Deusebio, E., Brethouwer, G., Schlatter, P. & Lindborg, E. 2014 A numerical study of the unstratified and stratified Ekman layer. J. Fluid Mech. 755, 672–704.Google Scholar
Duguet, Y. & Schlatter, P. 2013 Oblique laminar–turbulent interfaces in plane shear flows. Phys. Rev. Lett. 110, 034502.Google Scholar
Duguet, Y., Schlatter, P. & Henningson, D. S. 2010 Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech. 650, 119–129.CrossRefGoogle Scholar
Emmons, H. W. 1951 The laminar–turbulent transition in a boundary layer – Part I. J. Aero. Sci. 18 (7), 490–498.CrossRefGoogle Scholar
Fransson, J. H. M. & Alfredsson, P. H. 2003 On the disturbance growth in an asymptotic suction boundary layer. J. Fluid Mech. 482, 51–90.Google Scholar
Hall, P. & Smith, F. T. 1991 On strongly nonlinear vortex/wave interactions in boundary-layer transition. J. Fluid Mech. 227, 641–666.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.Google Scholar
Hegseth, J. J., Andereck, C. D., Hayot, F. & Pomeau, Y. 1989 Spiral turbulence and phase dynamics. Phys. Rev. Lett. 62 (3), 257–260.Google Scholar
Henningson, D. S., Spalart, P. R. & Kim, J. 1987 Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow. Phys. Fluids 30 (10), 2914–2917.Google Scholar
Hocking, L. M. 1975 Non-linear instability of the asymptotic suction velocity profile. Q. J. Mech. Appl. Maths 28 (3), 341–353.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Jiménez, J. 1998 The largest scales of turbulent wall flows. CTR Annu. Res. Briefs 137–154.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Kametani, Y., Fukagata, K., Örlü, R. & Schlatter, P. 2015 Effect of uniform blowing/suction in a turbulent boundary layer at moderate Reynolds number. Intl J. Heat Fluid Flow 55, 132–142.Google Scholar
Khapko, T.2014 Transition to turbulence in the asymptotic suction boundary layer. Licentiate Thesis, KTH Mechanics, Stockholm.Google Scholar
Khapko, T., Duguet, Y., Kreilos, T., Schlatter, P., Eckhardt, B. & Henningson, D. S. 2014 Complexity of localised coherent structures in a boundary-layer flow. Eur. Phys. J. E 37 (4), 32.Google Scholar
Khapko, T., Kreilos, T., Schlatter, P., Duguet, Y., Eckhardt, B. & Henningson, D. S. 2013 Localised edge states in the asymptotic suction boundary layer. J. Fluid Mech. 717, R6.Google Scholar
Kreilos, T., Khapko, T., Schlatter, P., Duguet, Y., Henningson, D. S. & Eckhardt, B. 2016 Bypass transition and spot nucleation in boundary layers. Phys. Rev. Fluids (submitted).Google Scholar
Kreilos, T., Veble, G., Schneider, T. M. & Eckhardt, B. 2013 Edge states for the turbulence transition in the asymptotic suction boundary layer. J. Fluid Mech. 726, 100–122.CrossRefGoogle Scholar
Lemoult, G., Shi, L., Avila, K., Jalikop, S. V., Avila, M. & Hof, B. 2016 Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys. 12, 254–258.Google Scholar
Levin, O. & Henningson, D. S. 2007 Turbulent spots in the asymptotic suction boundary layer. J. Fluid Mech. 584, 397–414.Google Scholar
Manneville, P. 2009 Spatiotemporal perspective on the decay of turbulence in wall-bounded flows. Phys. Rev. E 79, 025301.Google Scholar
Manneville, P. 2011 On the decay of turbulence in plane Couette flow. Fluid Dyn. Res. 43, 065501.Google Scholar
Manneville, P. & Rolland, J. 2011 On modelling transitional turbulent flows using under-resolved direct numerical simulations: the case of plane Couette flow. Theor. Comput. Fluid Dyn. 25, 407–420.Google Scholar
Mariani, P., Spalart, P. R. & Kollmann, W. 1993 Direct 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.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329, 193–196.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.Google Scholar
Moxey, D. & Barkley, D. 2010 Distinct large-scale turbulent-laminar states in transitional pipe flow. Proc. Natl Acad. Sci. USA 107 (18), 8091–8096.Google Scholar
Orlandi, P., Bernardini, M. & Pirozzoli, S. 2015 Poiseuille and Couette flows in the transitional and fully turbulent regime. J. Fluid Mech. 770, 424–441.Google Scholar
Philip, J. & Manneville, P. 2011 From temporal to spatiotemporal dynamics in transitional plane Couette flow. Phys. Rev. E 83, 036308.Google Scholar
Prigent, A.2001 La spirale turbulente: motif de grande longueur d’onde dans les écoulements cisaillés turbulents. PhD thesis, Université Paris XI, Paris.Google Scholar
Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & van Saarloos, W. 2002 Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89 (1), 014501.Google Scholar
Reynolds, G. A. & Saric, W. S. 1986 Experiments on the stability of the flat-plate boundary layer with suction. AIAA J. 24 (2), 202–207.Google Scholar
Sano, M. & Tamai, K. 2016 A universal transition to turbulence in channel flow. Nat. Phys. 12, 249–253.Google Scholar
Schlatter, P. & Örlü, R. 2010a Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.Google Scholar
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, 051704.Google Scholar
Schlatter, P. & Örlü, R. 2011 Turbulent asymptotic suction boundary layers studied by simulation. J. Phys.: Conf. Ser. 318, 022020.Google Scholar
Schlichting, H. 1987 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Seki, D. & Matsubara, M. 2012 Experimental investigation of relaminarizing and transitional channel flows. Phys. Fluids 24, 124102.Google Scholar
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.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D. 2005 DNS of turbulent channel flow at very low Reynolds numbers. In Fourth International Symposium on Turbulence and Shear Flow Phenomena, pp. 935–940.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.Google Scholar
Willis, A. P. & Kerswell, R. R. 2009 Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized ‘edge’ states. J. Fluid Mech. 619, 213–233.Google Scholar