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Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

Published online by Cambridge University Press:  07 February 2019

Benjamin Favier Open the ORCID record for Benjamin Favier [Opens in a new window] ,
Céline Guervilly Open the ORCID record for Céline Guervilly [Opens in a new window]  and
Edgar Knobloch
Benjamin Favier*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, Marseille, France
Céline Guervilly
Affiliation:
School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK
Edgar Knobloch
Affiliation:
Department of Physics, University of California, Berkeley, CA 94720, USA
*
†Email address for correspondence: [email protected]
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Abstract

The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. This new example of bistability in a turbulent flow, which may not be specific to rotating convection, opens up new avenues for studying energy transfer in strongly anisotropic three-dimensional flows such as atmospheric or oceanic circulations.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Turbulent Flows: Turbulent transition
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , R1
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Copyright
© 2019 Cambridge University Press 

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References

Alexakis, A. 2011 Two-dimensional behavior of three-dimensional magnetohydrodynamic flow with a strong guiding field. Phys. Rev. E 84, 056330.Google Scholar
Alexakis, A. 2015 Rotating Taylor–Green flow. J. Fluid Mech. 769, 46–78.Google Scholar
Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767–769, 1–101.Google Scholar
Bartello, P. 1995 Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci. 52, 4410–4428.Google Scholar
Benavides, S. J. & Alexakis, A. 2017 Critical transitions in thin layer turbulence. J. Fluid Mech. 822, 364–385.Google Scholar
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427–451.Google Scholar
Bouchet, F. & Simonnet, E. 2009 Random changes in flow topology in two-dimensional and geophysical turbulence. Phys. Rev. Lett. 102, 094504.Google Scholar
Campagne, A., Gallet, B., Moisy, F. & Cortet, P.-P. 2014 Direct and inverse energy cascades in a forced rotating turbulence experiment. Phys. Fluids 26, 125112.Google Scholar
Celani, A., Musacchio, S. & Vincenzi, D. 2010 Turbulence in more than two and less than three dimensions. Phys. Rev. Lett. 104, 184506.Google Scholar
Chertkov, M., Connaughton, C., Kolokolov, I. & Lebedev, V. 2007 Dynamics of energy condensation in two-dimensional turbulence. Phys. Rev. Lett. 99, 084501.Google Scholar
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114.Google Scholar
Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468.Google Scholar
Fauve, S., Herault, J., Michel, G. & Pétrélis, F. 2017 Instabilities on a turbulent background. J. Stat. Mech. 2017, 064001.Google Scholar
Favier, B., Godeferd, F. S., Cambon, C., Delache, A. & Bos, W. J. T. 2011 Quasi-static magnetohydrodynamic turbulence at high Reynolds number. J. Fluid Mech. 681, 434–461.Google Scholar
Favier, B., Silvers, L. J. & Proctor, M. R. E. 2014 Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection. Phys. Fluids 26, 096605.Google Scholar
Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G.2008 Nek5000: open source spectral element CFD solver. Available at https://nek5000.mcs.anl.gov.Google Scholar
Gallet, B. & Young, W. R. 2014 A two-dimensional vortex condensate at high Reynolds number. J. Fluid Mech. 715, 359–388.Google Scholar
Guervilly, C., Hughes, D. W. & Jones, C. A. 2014 Large-scale vortices in rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 758, 407–435.Google Scholar
Huisman, S. G., van der Veen, R. C. A., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5, 3820.Google Scholar
Julien, K., Knobloch, E. & Plumley, M. 2018 Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection. J. Fluid Mech. 837, R4.Google Scholar
Julien, K., Rubio, A. M., Grooms, I. & Knobloch, E. 2012 Statistical and physical balances in low Rossby number Rayleigh–Bénard convection. Geophys. Astrophys. Fluid Dyn. 106, 392–428.Google Scholar
van Kan, A. & Alexakis, A. 2019 Condensates in thin-layer turbulence. J. Fluid Mech. (in press) arXiv:1808.00578.Google Scholar
Kerswell, R. R. 2018 Nonlinear nonmodal stability theory. Annu. Rev. Fluid Mech. 50, 319–345.Google Scholar
Kraichnan, R. H. 1967 Inertial ranges in 2D turbulence. Phys. Fluids 10, 1417–1423.Google Scholar
Mujica, N. & Lathrop, D. P. 2006 Hysteretic gravity-wave bifurcation in a highly turbulent swirling flow. J. Fluid Mech. 551, 49–62.Google Scholar
Oks, D., Mininni, P. D., Marino, R. & Pouquet, A. 2017 Inverse cascades and resonant triads in rotating and stratified turbulence. Phys. Fluids 29, 111109.Google Scholar
Pouquet, A. & Marino, R. 2013 Geophysical turbulence and the duality of the energy flow across scales. Phys. Rev. Lett. 111, 234501.Google Scholar
Ravelet, F., Marié, L., Chiffaudel, A. & Daviaud, F. 2004 Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation. Phys. Rev. Lett. 93, 164501.Google Scholar
Rubio, A. M., Julien, K., Knobloch, E. & Weiss, J. B. 2014 Upscale energy transfer in three-dimensional rapidly rotating turbulent convection. Phys. Rev. Lett. 112, 144501.Google Scholar
Smith, L. & Yakhot, V. 1994 Finite-size effects in forced two-dimensional turbulence. J. Fluid Mech. 274, 115–138.Google Scholar
Smith, L. M., Chasnov, J. R. & Waleffe, F. 1996 Crossover from two- to three-dimensional turbulence. Phys. Rev. Lett. 77, 2467–2470.Google Scholar
Smith, L. M. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11, 1608–1622.Google Scholar
Smith, L. M. & Waleffe, F. 2002 Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145–168.Google Scholar
Xia, H., Byrne, D., Falkovich, G. & Shats, M. 2011 Upscale energy transfer in thick turbulent fluid layers. Nat. Phys. 7, 321–324.Google Scholar
Xia, H. & Francois, N. 2017 Two-dimensional turbulence in three-dimensional flows. Phys. Fluids 29, 111107.Google Scholar
Xia, Z., Shi, Y., Cai, Q., Wan, M. & Chen, S. 2018 Multiple states in turbulent plane Couette flow with spanwise rotation. J. Fluid Mech. 837, 477–490.Google Scholar
Yokoyama, N. & Takaoka, M. 2017 Hysteretic transitions between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence. Phys. Rev. Fluids 2, 092602.Google Scholar
Zimmerman, D. S., Triana, S. A. & Lathrop, D. P. 2011 Bi-stability in turbulent, rotating spherical Couette flow. Phys. Fluids 23, 065104.Google Scholar