zbMATH — the first resource for mathematics

Subcritical turbulent condensate in rapidly rotating Rayleigh-Bénard convection. (English) Zbl 1415.76269
Summary: 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.

76F06 Transition to turbulence
76F20 Dynamical systems approach to turbulence
76F35 Convective turbulence
76U05 General theory of rotating fluids
Full Text: DOI
[1] Alexakis, A., Two-dimensional behavior of three-dimensional magnetohydrodynamic flow with a strong guiding field, Phys. Rev. E, 84, (2011)
[2] Alexakis, A., Rotating Taylor-Green flow, J. Fluid Mech., 769, 46-78, (2015) · Zbl 1337.76070
[3] Alexakis, A.; Biferale, L., Cascades and transitions in turbulent flows, Phys. Rep., 767-769, 1-101, (2018)
[4] Bartello, P., Geostrophic adjustment and inverse cascades in rotating stratified turbulence, J. Atmos. Sci., 52, 4410-4428, (1995)
[5] Benavides, S. J.; Alexakis, A., Critical transitions in thin layer turbulence, J. Fluid Mech., 822, 364-385, (2017) · Zbl 1387.86026
[6] Boffetta, G.; Ecke, R. E., Two-dimensional turbulence, Annu. Rev. Fluid Mech., 44, 427-451, (2012) · Zbl 1350.76022
[7] Bouchet, F.; Simonnet, E., Random changes in flow topology in two-dimensional and geophysical turbulence, Phys. Rev. Lett., 102, (2009)
[8] Campagne, A.; Gallet, B.; Moisy, F.; Cortet, P.-P., Direct and inverse energy cascades in a forced rotating turbulence experiment, Phys. Fluids, 26, (2014)
[9] Celani, A.; Musacchio, S.; Vincenzi, D., Turbulence in more than two and less than three dimensions, Phys. Rev. Lett., 104, (2010)
[10] Chertkov, M.; Connaughton, C.; Kolokolov, I.; Lebedev, V., Dynamics of energy condensation in two-dimensional turbulence, Phys. Rev. Lett., 99, (2007)
[11] Darbyshire, A. G.; Mullin, T., Transition to turbulence in constant-mass-flux pipe flow, J. Fluid Mech., 289, 83-114, (1995)
[12] Eckhardt, B.; Schneider, T. M.; Hof, B.; Westerweel, J., Turbulence transition in pipe flow, Annu. Rev. Fluid Mech., 39, 447-468, (2007) · Zbl 1296.76062
[13] Fauve, S.; Herault, J.; Michel, G.; Pétrélis, F., Instabilities on a turbulent background, J. Stat. Mech., 2017, (2017)
[14] Favier, B.; Godeferd, F. S.; Cambon, C.; Delache, A.; Bos, W. J. T., Quasi-static magnetohydrodynamic turbulence at high Reynolds number, J. Fluid Mech., 681, 434-461, (2011) · Zbl 1241.76293
[15] Favier, B.; Silvers, L. J.; Proctor, M. R. E., Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection, Phys. Fluids, 26, (2014) · Zbl 1323.76106
[16] Fischer, P. F.; Lottes, J. W.; Kerkemeier, S. G.
[17] Gallet, B.; Young, W. R., A two-dimensional vortex condensate at high Reynolds number, J. Fluid Mech., 715, 359-388, (2014) · Zbl 1284.76108
[18] Guervilly, C.; Hughes, D. W.; Jones, C. A., Large-scale vortices in rapidly rotating Rayleigh-Bénard convection, J. Fluid Mech., 758, 407-435, (2014)
[19] Huisman, S. G.; Van Der Veen, R. C. A.; Sun, C.; Lohse, D., Multiple states in highly turbulent Taylor-Couette flow, Nat. Commun., 5, 3820, (2014)
[20] Julien, K.; Knobloch, E.; Plumley, M., Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection, J. Fluid Mech., 837, R4, (2018)
[21] Julien, K.; Rubio, A. M.; Grooms, I.; Knobloch, E., Statistical and physical balances in low Rossby number Rayleigh-Bénard convection, Geophys. Astrophys. Fluid Dyn., 106, 392-428, (2012)
[22] Van Kan, A.; Alexakis, A., Condensates in thin-layer turbulence, J. Fluid Mech., (2019)
[23] Kerswell, R. R., Nonlinear nonmodal stability theory, Annu. Rev. Fluid Mech., 50, 319-345, (2018) · Zbl 1384.76022
[24] Kraichnan, R. H., Inertial ranges in 2D turbulence, Phys. Fluids, 10, 1417-1423, (1967)
[25] Mujica, N.; Lathrop, D. P., Hysteretic gravity-wave bifurcation in a highly turbulent swirling flow, J. Fluid Mech., 551, 49-62, (2006) · Zbl 1119.76306
[26] Oks, D.; Mininni, P. D.; Marino, R.; Pouquet, A., Inverse cascades and resonant triads in rotating and stratified turbulence, Phys. Fluids, 29, (2017)
[27] Pouquet, A.; Marino, R., Geophysical turbulence and the duality of the energy flow across scales, Phys. Rev. Lett., 111, (2013)
[28] Ravelet, F.; Marié, L.; Chiffaudel, A.; Daviaud, F., Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation, Phys. Rev. Lett., 93, (2004)
[29] Rubio, A. M.; Julien, K.; Knobloch, E.; Weiss, J. B., Upscale energy transfer in three-dimensional rapidly rotating turbulent convection, Phys. Rev. Lett., 112, (2014)
[30] Smith, L.; Yakhot, V., Finite-size effects in forced two-dimensional turbulence, J. Fluid Mech., 274, 115-138, (1994) · Zbl 0825.76356
[31] Smith, L. M.; Chasnov, J. R.; Waleffe, F., Crossover from two- to three-dimensional turbulence, Phys. Rev. Lett., 77, 2467-2470, (1996)
[32] Smith, L. M.; Waleffe, F., Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence, Phys. Fluids, 11, 1608-1622, (1999) · Zbl 1147.76500
[33] Smith, L. M.; Waleffe, F., Generation of slow large scales in forced rotating stratified turbulence, J. Fluid Mech., 451, 145-168, (2002) · Zbl 1009.76040
[34] Xia, H.; Byrne, D.; Falkovich, G.; Shats, M., Upscale energy transfer in thick turbulent fluid layers, Nat. Phys., 7, 321-324, (2011)
[35] Xia, H.; Francois, N., Two-dimensional turbulence in three-dimensional flows, Phys. Fluids, 29, (2017)
[36] Xia, Z.; Shi, Y.; Cai, Q.; Wan, M.; Chen, S., Multiple states in turbulent plane Couette flow with spanwise rotation, J. Fluid Mech., 837, 477-490, (2018)
[37] Yokoyama, N.; Takaoka, M., Hysteretic transitions between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence, Phys. Rev. Fluids, 2, (2017)
[38] Zimmerman, D. S.; Triana, S. A.; Lathrop, D. P., Bi-stability in turbulent, rotating spherical Couette flow, Phys. Fluids, 23, (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.