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Edge states as mediators of bypass transition in boundary-layer flows

  • T. Khapko (a1) (a2), T. Kreilos (a3), P. Schlatter (a1) (a2), Y. Duguet (a4), B. Eckhardt (a5) (a6) and D. S. Henningson (a1) (a2)...

Abstract

The concept of edge states is investigated in the asymptotic suction boundary layer in relation to the receptivity process to noisy perturbations and the nucleation of turbulent spots. Edge tracking is first performed numerically, without imposing any discrete symmetry, in a large computational domain allowing for full spatial localisation of the perturbation velocity. The edge state is a three-dimensional localised structure recurrently characterised by a single low-speed streak that experiences erratic bursts and planar shifts. This recurrent streaky structure is then compared with predecessors of individual spot nucleation events, triggered by non-localised initial noise. The present results suggest a nonlinear picture, rooted in dynamical systems theory, of the nucleation process of turbulent spots in boundary-layer flows, in which the localised edge state plays the role of state-space mediator.

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Corresponding author

Email address for correspondence: pschlatt@mech.kth.se

References

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Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 2960.
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, 217240.
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167198.
Cherubini, S., De Palma, P., Robinet, J. C. & Bottaro, A. 2011 Edge states in a boundary layer. Phys. Fluids 23, 051705.
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.
Duguet, Y., Monokrousos, A., Brandt, L. & Henningson, D. S. 2013 Minimal transition thresholds in plane Couette flow. Phys. Fluids 25, 084103.
Duguet, Y., Schlatter, P. & Henningson, D. S. 2009 Localized edge states in plane Couette flow. Phys. Fluids 21, 111701.
Duguet, Y., Schlatter, P. & Henningson, D. S. 2010a Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech. 650, 119129.
Duguet, Y., Schlatter, P., Henningson, D. S. & Eckhardt, B. 2012 Self-sustained localized structures in a boundary-layer flow. Phys. Rev. Lett. 108, 044501.
Duguet, Y., Willis, A. P. & Kerswell, R. R. 2010b Slug genesis in cylindrical pipe flow. J. Fluid Mech. 663, 180208.
Emmons, H. W. 1951 The laminar–turbulent transition in a boundary layer – Part I. J. Aero. Sci. 18 (7), 490498.
Fransson, J. H. M. & Alfredsson, P. H. 2003 On the disturbance growth in an asymptotic suction boundary layer. J. Fluid Mech. 482, 5190.
Griffith, A. A. & Meredith, F. W.1936 The possible improvement in aircraft performance due to the use of boundary layer suction. Tech. Rep. 3501. Royal Aircraft Establishment.
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Hocking, L. M. 1975 Non-linear instability of the asymptotic suction velocity profile. Q. J. Mech. Appl. Maths 28 (3), 341353.
Itano, T. & Toh, S. 2001 The dynamics of bursting process in wall turbulence. J. Phys. Soc. Japan 70, 703716.
Kendall, J. M. 1998 Experiments on boundary-layer receptivity to free-stream turbulence. AIAA Paper 980530.
Kerswell, R. R., Pringle, C. C. T. & Willis, A. P. 2014 An optimization approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar. Rep. Prog. Phys. 77, 085901.
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.
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.
Khapko, T., Schlatter, P., Duguet, Y. & Henningson, D. S. 2016 Turbulence collapse in a suction boundary layer. J. Fluid Mech. 795, 356379.
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 (to appear).
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, 100122.
Matsubara, M. & Alfredsson, P. H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149168.
Mellibovsky, F., Meseguer, A., Schneider, T. M. & Eckhardt, B. 2009 Transition in localized pipe flow turbulence. Phys. Rev. Lett. 103, 054502.
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291319.
Schlatter, P., Brandt, L., De Lange, H. C. & Henningson, D. S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20, 101505.
Schneider, T. M., Eckhardt, B. & Yorke, J. A. 2007 Turbulence transition and the edge of chaos in pipe flow. Phys. Rev. Lett. 99, 034502.
Schneider, T. M., Marinc, D. & Eckhardt, B. 2010 Localized edge states nucleate turbulence in extended plane Couette cells. J. Fluid Mech. 646, 441451.
Skufca, J. D., Yorke, J. A. & Eckhardt, B. 2006 Edge of chaos in a parallel shear flow. Phys. Rev. Lett. 96, 174101.
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, 213233.
Yoshioka, S., Fransson, J. H. M. & Alfredsson, P. H. 2004 Free stream turbulence induced disturbances in boundary layers with wall suction. Phys. Fluids 16 (10), 35303539.
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85111.
Zammert, S. & Eckhardt, B. 2014 Streamwise and doubly-localised periodic orbits in plane Poiseuille flow. J. Fluid Mech. 761, 348359.
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Edge states as mediators of bypass transition in boundary-layer flows

  • T. Khapko (a1) (a2), T. Kreilos (a3), P. Schlatter (a1) (a2), Y. Duguet (a4), B. Eckhardt (a5) (a6) and D. S. Henningson (a1) (a2)...

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