Skip to main content Accessibility help
×
Home

Diffusive dynamics and stochastic models of turbulent axisymmetric wakes

  • G. Rigas (a1), A. S. Morgans (a1), R. D. Brackston (a1) and J. F. Morrison (a1)

Abstract

A modelling methodology to reproduce the experimental measurements of a turbulent flow in the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
      Available formats
      ×

Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

References

Hide All
Berhanu, M., Gallet, B., Monchaux, R., Bourgoin, M., Odier, Ph., Pinton, J.-F., Plihon, N., Volk, R., Fauve, S., Mordant, N., Pétrélis, F., Aumaître, S., Chiffaudel, A., Daviaud, F., Dubrulle, B. & Ravelet, F. 2009 Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium. J. Fluid Mech. 641, 217226.
Bobinski, T., Goujon-Durand, S. & Wesfreid, J. E. 2014 Instabilities in the wake of a circular disk. Phys. Rev. E 89, 053021.
Bohorquez, P., Sanmiguel-Rojas, E., Sevilla, A., Jiménez-González, J. I. & Martínez-Bazán, C. 2011 Stability and dynamics of the laminar wake past a slender blunt-based axisymmetric body. J. Fluid Mech. 676, 110144.
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351386.
Brown, E. & Ahlers, G. 2007 Large-scale circulation model for turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98 (13), 134501.
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95 (8), 084503.
Bury, Y. & Jardin, T. 2012 Transitions to chaos in the wake of an axisymmetric bluff body. Phys. Lett. A 376, 32193222.
Crawford, J. D. & Knobloch, E. 1991 Symmetry and symmetry-breaking bifurcations in fluid dynamics. Annu. Rev. Fluid Mech. 23 (1), 341387.
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.
Einstein, A. 1905 Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 322 (8), 549560.
Fabre, D., Auguste, F. & Magnaudet, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20 (5), 051702.
Frisch, U. 1996 Turbulence. Cambridge University Press.
Gardiner, C. W. 1985 Stochastic Methods. Springer.
Grandemange, M., Cadot, O. & Gohlke, M. 2012 Reflectional symmetry breaking of the separated flow over three-dimensional bluff bodies. Phys. Rev. E 86, 035302.
Grandemange, M., Gohlke, M. & Cadot, O. 2013 Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability. J. Fluid Mech. 722, 5184.
Grandemange, M., Gohlke, M. & Cadot, O. 2014 Statistical axisymmetry of the turbulent sphere wake. Exp. Fluids 55 (11), 111.
Holmes, P., Lumley, J. L., Berkooz, G. & Rowley, C. W. 2012 Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 2nd edn. Cambridge University Press.
Meliga, P., Chomaz, J.-M. & Sipp, D. 2009 Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion. J. Fluid Mech. 633, 159189.
Mittal, R., Wilson, J. J. & Najjar, F. M. 2002 Symmetry properties of the transitional sphere wake. AIAA J. 40 (3), 579582.
Oxlade, A. R., Morrison, J. F., Qubain, A. & Rigas, G. 2015 High-frequency forcing of a turbulent axisymmetric wake. J. Fluid Mech. 770, 305318.
Pétrélis, F., Fauve, S., Dormy, E. & Valet, J. 2009 Simple mechanism for reversals of Earth’s magnetic field. Phys. Rev. Lett. 102 (14), 144503.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Rigas, G., Oxlade, A. R., Morgans, A. S. & Morrison, J. F. 2014 Low-dimensional dynamics of a turbulent axisymmetric wake. J. Fluid Mech. 755, R5.
Sreenivasan, K. R., Bershadskii, A. & Niemela, J. J. 2002 Mean wind and its reversal in thermal convection. Phys. Rev. E 65, 056306.
de la Torre, A. & Burguete, J. 2007 Slow dynamics in a turbulent von Kármán swirling flow. Phys. Rev. Lett. 99 (5), 054101.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Diffusive dynamics and stochastic models of turbulent axisymmetric wakes

  • G. Rigas (a1), A. S. Morgans (a1), R. D. Brackston (a1) and J. F. Morrison (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed