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Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

  • Benjamin Favier (a1), Céline Guervilly (a2) and Edgar Knobloch (a3)


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.


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Alexakis, A. 2011 Two-dimensional behavior of three-dimensional magnetohydrodynamic flow with a strong guiding field. Phys. Rev. E 84, 056330.
Alexakis, A. 2015 Rotating Taylor–Green flow. J. Fluid Mech. 769, 4678.
Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767–769, 1101.
Bartello, P. 1995 Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci. 52, 44104428.
Benavides, S. J. & Alexakis, A. 2017 Critical transitions in thin layer turbulence. J. Fluid Mech. 822, 364385.
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427451.
Bouchet, F. & Simonnet, E. 2009 Random changes in flow topology in two-dimensional and geophysical turbulence. Phys. Rev. Lett. 102, 094504.
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.
Celani, A., Musacchio, S. & Vincenzi, D. 2010 Turbulence in more than two and less than three dimensions. Phys. Rev. Lett. 104, 184506.
Chertkov, M., Connaughton, C., Kolokolov, I. & Lebedev, V. 2007 Dynamics of energy condensation in two-dimensional turbulence. Phys. Rev. Lett. 99, 084501.
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83114.
Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447468.
Fauve, S., Herault, J., Michel, G. & Pétrélis, F. 2017 Instabilities on a turbulent background. J. Stat. Mech. 2017, 064001.
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, 434461.
Favier, B., Silvers, L. J. & Proctor, M. R. E. 2014 Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection. Phys. Fluids 26, 096605.
Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G.2008 Nek5000: open source spectral element CFD solver. Available at
Gallet, B. & Young, W. R. 2014 A two-dimensional vortex condensate at high Reynolds number. J. Fluid Mech. 715, 359388.
Guervilly, C., Hughes, D. W. & Jones, C. A. 2014 Large-scale vortices in rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 758, 407435.
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.
Julien, K., Knobloch, E. & Plumley, M. 2018 Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection. J. Fluid Mech. 837, R4.
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, 392428.
van Kan, A. & Alexakis, A. 2019 Condensates in thin-layer turbulence. J. Fluid Mech. (in press) arXiv:1808.00578.
Kerswell, R. R. 2018 Nonlinear nonmodal stability theory. Annu. Rev. Fluid Mech. 50, 319345.
Kraichnan, R. H. 1967 Inertial ranges in 2D turbulence. Phys. Fluids 10, 14171423.
Mujica, N. & Lathrop, D. P. 2006 Hysteretic gravity-wave bifurcation in a highly turbulent swirling flow. J. Fluid Mech. 551, 4962.
Oks, D., Mininni, P. D., Marino, R. & Pouquet, A. 2017 Inverse cascades and resonant triads in rotating and stratified turbulence. Phys. Fluids 29, 111109.
Pouquet, A. & Marino, R. 2013 Geophysical turbulence and the duality of the energy flow across scales. Phys. Rev. Lett. 111, 234501.
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.
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.
Smith, L. & Yakhot, V. 1994 Finite-size effects in forced two-dimensional turbulence. J. Fluid Mech. 274, 115138.
Smith, L. M., Chasnov, J. R. & Waleffe, F. 1996 Crossover from two- to three-dimensional turbulence. Phys. Rev. Lett. 77, 24672470.
Smith, L. M. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11, 16081622.
Smith, L. M. & Waleffe, F. 2002 Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145168.
Xia, H., Byrne, D., Falkovich, G. & Shats, M. 2011 Upscale energy transfer in thick turbulent fluid layers. Nat. Phys. 7, 321324.
Xia, H. & Francois, N. 2017 Two-dimensional turbulence in three-dimensional flows. Phys. Fluids 29, 111107.
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, 477490.
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.
Zimmerman, D. S., Triana, S. A. & Lathrop, D. P. 2011 Bi-stability in turbulent, rotating spherical Couette flow. Phys. Fluids 23, 065104.
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