Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-08-19T08:28:43.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Bistability of the large-scale dynamics in quasi-two-dimensional turbulence

Published online by Cambridge University Press:  24 March 2022

Xander M. de Wit Open the ORCID record for Xander M. de Wit [Opens in a new window] ,
Adrian van Kan Open the ORCID record for Adrian van Kan [Opens in a new window]  and
Alexandros Alexakis Open the ORCID record for Alexandros Alexakis [Opens in a new window]
Xander M. de Wit
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France Fluids and Flows Group, Department of Applied Physics, and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Adrian van Kan
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France Department of Physics, University of California, Berkeley, CA 94720, USA
Alexandros Alexakis*
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
*
†Email address for correspondence: alexandros.alexakis@phys.ens.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-two-dimensional upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular three-dimensional state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number $Re$ are increased, showing that the bistability is neither a finite-size nor a finite-$Re$ effect. We furthermore predict a cross-over from a bimodal regime at low box size, low $Re$ to a regime of pure hysteresis at high box size, high $Re$, in which any transition from one state to the other is prohibited at any finite time scale.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent transition

Information

Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 939 , 25 May 2022 , R2
Check for updates
Copyright
© The Author(s), 2022. Published by 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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Aguirre Guzmán, A.J., Madonia, M., Cheng, J.S., Ostilla-Mónico, R., Clercx, H.J.H. & Kunnen, R.P.J. 2020 Competition between Ekman plumes and vortex condensates in rapidly rotating thermal convection. Phys. Rev. Lett. 125 (21), 214501.10.1103/PhysRevLett.125.214501CrossRefGoogle ScholarPubMed
Alexakis, A. 2011 Two-dimensional behavior of three-dimensional magnetohydrodynamic flow with a strong guiding field. Phys. Rev. E 84 (5), 056330.10.1103/PhysRevE.84.056330CrossRefGoogle ScholarPubMed
Alexakis, A. 2015 Rotating Taylor–Green flow. J. Fluid Mech. 769, 46–78.10.1017/jfm.2015.82CrossRefGoogle Scholar
Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767–769, 1–101.10.1016/j.physrep.2018.08.001CrossRefGoogle Scholar
Baker, N.T., Pothérat, A., Davoust, L. & Debray, F. 2018 Inverse and direct energy cascades in three-dimensional magnetohydrodynamic turbulence at low magnetic Reynolds number. Phys. Rev. Lett. 120 (22), 224502.10.1103/PhysRevLett.120.224502CrossRefGoogle ScholarPubMed
Batchelor, G.K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 12 (12), II-233–II-239.10.1063/1.1692443CrossRefGoogle Scholar
Benavides, S.J. & Alexakis, A. 2017 Critical transitions in thin layer turbulence. J. Fluid Mech. 822, 364–385.10.1017/jfm.2017.293CrossRefGoogle Scholar
Biferale, L., Bonaccorso, F., Mazzitelli, I.M., van Hinsberg, M.A.T., Lanotte, A.S., Musacchio, S., Perlekar, P. & Toschi, F. 2016 Coherent structures and extreme events in rotating multiphase turbulent flows. Phys. Rev. X 6 (4), 041036.Google Scholar
Bouchet, F., Rolland, J. & Simonnet, E. 2019 Rare event algorithm links transitions in turbulent flows with activated nucleations. Phys. Rev. Lett. 122 (7), 074502.10.1103/PhysRevLett.122.074502CrossRefGoogle ScholarPubMed
Byrne, D. & Zhang, J.A. 2013 Height-dependent transition from 3-D to 2-D turbulence in the hurricane boundary layer. Geophys. Res. Lett. 40 (7), 1439–1442.10.1002/grl.50335CrossRefGoogle Scholar
Celani, A., Musacchio, S. & Vincenzi, D. 2010 Turbulence in more than two and less than three dimensions. Phys. Rev. Lett. 104 (18), 184506.10.1103/PhysRevLett.104.184506CrossRefGoogle ScholarPubMed
Cérou, F. & Guyader, A. 2007 Adaptive multilevel splitting for rare event analysis. Stoch. Anal. Applics. 25 (2), 417–443.10.1080/07362990601139628CrossRefGoogle Scholar
Favier, B., Godeferd, F.S., Cambon, C. & Delache, A. 2010 On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence. Phys. Fluids 22 (7), 075104.10.1063/1.3456725CrossRefGoogle Scholar
Favier, B., Guervilly, C. & Knobloch, E. 2019 Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 864, R1.10.1017/jfm.2019.58CrossRefGoogle Scholar
Favier, B., Silvers, L.J. & Proctor, M.R.E. 2014 Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection. Phys. Fluids 26 (9), 096605.10.1063/1.4895131CrossRefGoogle Scholar
Goldenfeld, N., Guttenberg, N. & Gioia, G. 2010 Extreme fluctuations and the finite lifetime of the turbulent state. Phys. Rev. E 81, 035304(R).10.1103/PhysRevE.81.035304CrossRefGoogle ScholarPubMed
Gomé, S., Tuckerman, L.S. & Barkley, D. 2022 Extreme events in transitional turbulence. arXiv:2109.01476.Google Scholar
Guervilly, C., Hughes, D.W. & Jones, C.A. 2014 Large-scale vortices in rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 758, 407–435.10.1017/jfm.2014.542CrossRefGoogle Scholar
Heimpel, M. & Aurnou, J. 2007 Turbulent convection in rapidly rotating spherical shells: a model for equatorial and high latitude jets on Jupiter and Saturn. Icarus 187 (2), 540–557.10.1016/j.icarus.2006.10.023CrossRefGoogle Scholar
Heimpel, M., Gastine, T. & Wicht, J. 2016 Simulation of deep-seated zonal jets and shallow vortices in gas giant atmospheres. Nat. Geosci. 9 (1), 19–23.10.1038/ngeo2601CrossRefGoogle 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 (4–5), 392–428.10.1080/03091929.2012.696109CrossRefGoogle Scholar
van Kan, A. & Alexakis, A. 2019 Condensates in thin-layer turbulence. J. Fluid Mech. 864, 490–518.10.1017/jfm.2019.29CrossRefGoogle Scholar
van Kan, A. & Alexakis, A. 2020 Critical transition in fast-rotating turbulence within highly elongated domains. J. Fluid Mech. 899, A33.10.1017/jfm.2020.443CrossRefGoogle Scholar
van Kan, A., Nemoto, T. & Alexakis, A. 2019 Rare transitions to thin-layer turbulent condensates. J. Fluid Mech. 878, 356–369.10.1017/jfm.2019.572CrossRefGoogle Scholar
King, G.P., Vogelzang, J. & Stoffelen, A. 2015 Upscale and downscale energy transfer over the tropical Pacific revealed by scatterometer winds. J. Geophys. Res.: Oceans 120 (1), 346–361.10.1002/2014JC009993CrossRefGoogle Scholar
Kraichnan, R.H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (7), 1417–1423.10.1063/1.1762301CrossRefGoogle Scholar
Lestang, T., Ragone, F., Bréhier, C.-E., Herbert, C. & Bouchet, F. 2018 Computing return times or return periods with rare event algorithms. J. Stat. Mech.: Theory Exp. 4 (4), 043213.10.1088/1742-5468/aab856CrossRefGoogle Scholar
Marino, R., Mininni, P.D., Rosenberg, D. & Pouquet, A. 2013 Inverse cascades in rotating stratified turbulence: fast growth of large scales. Europhys. Lett. 102 (4), 44006.10.1209/0295-5075/102/44006CrossRefGoogle Scholar
Marino, R., Mininni, P.D., Rosenberg, D.L. & Pouquet, A. 2014 Large-scale anisotropy in stably stratified rotating flows. Phys. Rev. E 90 (2), 023018.10.1103/PhysRevE.90.023018CrossRefGoogle ScholarPubMed
Mininni, P.D., Alexakis, A. & Pouquet, A. 2009 Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers. Phys. Fluids 21 (1), 015108.10.1063/1.3064122CrossRefGoogle Scholar
Mininni, P.D., Rosenberg, D., Reddy, R. & Pouquet, A. 2011 A hybrid MPI–OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence. Parallel Comput. 37 (6–7), 316–326.10.1016/j.parco.2011.05.004CrossRefGoogle Scholar
Musacchio, S. & Boffetta, G. 2017 Split energy cascade in turbulent thin fluid layers. Phys. Fluids 29 (11), 111106.10.1063/1.4986001CrossRefGoogle Scholar
Musacchio, S. & Boffetta, G. 2019 Condensate in quasi-two-dimensional turbulence. Phys. Rev. Fluids 4 (2), 022602(R).10.1103/PhysRevFluids.4.022602CrossRefGoogle Scholar
Nastrom, G.D., Gage, K.S. & Jasperson, W.H. 1984 Kinetic energy spectrum of large-and mesoscale atmospheric processes. Nature 310 (5972), 36–38.10.1038/310036a0CrossRefGoogle Scholar
Nemoto, T. & Alexakis, A. 2018 Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows. Phys. Rev. E 97, 022207.10.1103/PhysRevE.97.022207CrossRefGoogle ScholarPubMed
Nemoto, T. & Alexakis, A. 2021 Do extreme events trigger turbulence decay? – A numerical study of turbulence decay time in pipe flows. J. Fluid Mech. 912, A38.10.1017/jfm.2020.1150CrossRefGoogle Scholar
Novikov, E.A. 1965 Functionals and the random-force method in turbulence theory. Sov. Phys. JETP 20 (5), 1290–1294.Google Scholar
Poujol, B., van Kan, A. & Alexakis, A. 2020 Role of the forcing dimensionality in thin-layer turbulent energy cascades. Phys. Rev. Fluids 5 (6), 064610.10.1103/PhysRevFluids.5.064610CrossRefGoogle Scholar
Pouquet, A. & Marino, R. 2013 Geophysical turbulence and the duality of the energy flow across scales. Phys. Rev. Lett. 111 (23), 234501.10.1103/PhysRevLett.111.234501CrossRefGoogle Scholar
Reddy, K.S., Kumar, R. & Verma, M.K. 2014 Anisotropic energy transfers in quasi-static magnetohydrodynamic turbulence. Phys. Plasmas 21 (10), 102310.10.1063/1.4899202CrossRefGoogle Scholar
Rolland, J. 2018 Extremely rare collapse and build-up of turbulence in stochastic models of transitional wall flows. Phys. Rev. E 97 (2), 023109.10.1103/PhysRevE.97.023109CrossRefGoogle ScholarPubMed
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 (14), 144501.10.1103/PhysRevLett.112.144501CrossRefGoogle ScholarPubMed
Scott, R.B. & Wang, F. 2005 Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J. Phys. Oceanogr. 35 (9), 1650–1666.10.1175/JPO2771.1CrossRefGoogle Scholar
Seshasayanan, K. & Alexakis, A. 2018 Condensates in rotating turbulent flows. J. Fluid Mech. 841, 434–462.10.1017/jfm.2018.106CrossRefGoogle Scholar
Smith, L.M., Chasnov, J.R. & Waleffe, F. 1996 Crossover from two- to three-dimensional turbulence. Phys. Rev. Lett. 77 (12), 2467–2470.10.1103/PhysRevLett.77.2467CrossRefGoogle ScholarPubMed
Smith, L.M. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11 (6), 1608–1622.10.1063/1.870022CrossRefGoogle Scholar
Stellmach, S., Verhoeven, J., Lischper, M. & Hansen, U. 2016 Towards a better understanding of rotating turbulent convection in geo- and astrophysical systems. In NIC Symposium 2016 (ed. K. Binder, M. Müller, M. Kremer & A. Schnurpfeil), paper FZJ-2016-02088. Jülich.Google Scholar
de Wit, X.M., Aguirre Guzmán, A.J., Clercx, H.J.H. & Kunnen, R.P.J. 2022 Discontinuous transitions towards vortex condensates in buoyancy-driven rotating turbulence. J. Fluid Mech. 936, A43.10.1017/jfm.2022.90CrossRefGoogle 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 (9), 092602(R).10.1103/PhysRevFluids.2.092602CrossRefGoogle Scholar