Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-24T00:41:26.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Localized travelling waves in the asymptotic suction boundary layer

Published online by Cambridge University Press:  20 April 2016

Tobias Kreilos ,
John F. Gibson  and
Tobias M. Schneider
Tobias Kreilos*
Affiliation:
Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne,  1015 Lausanne, Switzerland
John F. Gibson
Affiliation:
Department of Mathematics and Statistics, University of New Hampshire, Durham,  NH 03824, USA
Tobias M. Schneider*
Affiliation:
Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne,  1015 Lausanne, Switzerland
*
†Email addresses for correspondence: tobias.kreilos@epfl.ch, tobias.schneider@epfl.ch
†Email addresses for correspondence: tobias.kreilos@epfl.ch, tobias.schneider@epfl.ch
Get access Rights & Permissions [Opens in a new window]

Abstract

We present two spanwise-localized travelling-wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwise-localized edge states previously found for this system. The vortical structures of the second solution are located in the free stream far above the laminar boundary layer and are supported by a secondary shear gradient that is created by a large-scale low-speed streak. The dynamically relevant eigenmodes of this solution are concentrated in the free stream, and the departure into turbulence from this solution evolves in the free stream towards the walls. For invariant solutions in free-stream turbulence, this solution thus shows that the source of energy of the vortical structures can be a dynamical structure of the solution itself, instead of the laminar boundary layer.

JFM classification

Boundary Layers: Boundary Layers Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , R3
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

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Brand, E. & Gibson, J. F. 2014 A doubly-localized equilibrium solution of plane Couette flow. J. Fluid Mech. 750, R3.Google Scholar
Deguchi, K. & Hall, P. 2014 Free-stream coherent structures in parallel boundary-layer flows. J. Fluid Mech. 752, 602–625.CrossRefGoogle Scholar
Deguchi, K. & Hall, P. 2015a Asymptotic descriptions of oblique coherent structures in shear flows. J. Fluid Mech. 782, 356–367.Google Scholar
Deguchi, K. & Hall, P. 2015b Free-stream coherent structures in growing boundary layers: a link to near-wall streaks. J. Fluid Mech. 778, 451–484.Google Scholar
Gibson, J. F.2012, Channelflow: a spectral Navier–Stokes simulator in $\text{C}++$ . Tech. Rep. University of New Hampshire.Google Scholar
Gibson, J. F. & Brand, E. 2014 Spanwise-localized solutions of planar shear flows. J. Fluid Mech. 745, 25–61.Google Scholar
Gibson, J. F., Halcrow, J. & Cvitanović, P. 2009 Equilibrium and traveling-wave solutions of plane Couette flow. J. Fluid Mech. 638, 243–266.Google Scholar
Hall, P. & Sherwin, S. 2010 Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures. J. Fluid Mech. 661, 178–205.CrossRefGoogle 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
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Kawahara, G., Uhlmann, M. & van Veen, L. 2012 The significance of simple invariant solutions in turbulent flows. Annu. Rev. Fluid Mech. 44 (1), 203–225.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.CrossRefGoogle Scholar
Khapko, T., Kreilos, T., Schlatter, P., Duguet, Y., Eckhardt, B. & Henningson, D. S. 2013 Localized edge states in the asymptotic suction boundary layer. J. Fluid Mech. 717, R6.CrossRefGoogle 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
Levin, O. & Henningson, D. S. 2007 Turbulent spots in the asymptotic suction boundary layer. J. Fluid Mech. 584, 397–413.Google Scholar
Nagata, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519–527.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Schlatter, P & Örlü, R 2011 Turbulent asymptotic suction boundary layers studied by simulation. J. Phys.: Conf. Ser. 318 (2), 022020.Google Scholar
Schlichting, H. 2004 Boundary-Layer Theory. Springer.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Viswanath, D. 2007 Recurrent motions within plane Couette turbulence. J. Fluid Mech. 580, 339–358.Google Scholar
Viswanath, D. 2009 The critical layer in pipe flow at high Reynolds number. Phil. Trans. R. Soc. Lond. A 367 (1888), 561–576.Google Scholar
Waleffe, F 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.Google Scholar
Zammert, S. & Eckhardt, B. 2014 Streamwise and doubly-localised periodic orbits in plane Poiseuille flow. J. Fluid Mech. 761, 348–359.Google Scholar

Kreilos et al. supplementay movie

Time evolution of FCS in the downstream-averaged cross-flow energy in the y-z plane. We see the slow evolution of disturbances around the vortical structures and their slow spreading towards the wall and in the spanwise direction. Once the laminar boundary layer is reached, the disturbances become much more violent and spread much faster in the spanwise direction

Download Kreilos et al. supplementay movie(Video)
Video 2.8 MB