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Research Article

The geostrophic regime of rapidly rotating turbulent convection

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Pages 267-296 | Received 15 Sep 2020, Accepted 08 Dec 2020, Published online: 26 Jan 2021

References

  • Gill AE. Atmosphere–ocean dynamics. New York: Academic Press; 1982.
  • Hadley G. Concerning the cause of the general trade-winds. Phil Trans R Soc Lond. 1735;39:58–62.
  • Marshall J, Schott F. Open-ocean convection: observations, theory, and models. Rev Geophys. 1999;37:1–64.
  • Roberts PH, King EM. On the genesis of the Earth's magnetism. Rep Prog Phys. 2013;76:096801.
  • Aurnou JM, Calkins MA, Cheng JS, et al. Rotating convective turbulence in Earth and planetary cores. Phys Earth Planet Inter. 2015;246:52–71.
  • Jones CA. Planetary magnetic fields and fluid dynamos. Annu Rev Fluid Mech. 2011;43:583–614.
  • Olson P. Experimental dynamos and the dynamics of planetary cores. Annu Rev Earth Planet Sci. 2013;41:153–181.
  • Ingersoll AP. Atmospheric dynamics of the outer planets. Science. 1990;248:308–315.
  • Galperin B, Read PL. Zonal jets: phenomenology, genesis and physics. Cambridge: Cambridge University Press; 2019.
  • Miesch MS. The coupling of solar convection and rotation. Solar Phys. 2000;192:59–89.
  • Gubbins D. The Rayleigh number for convection in the Earth's core. Phys Earth Planet Inter. 2001;128:3–12.
  • Schubert G, Soderlund KM. Planetary magnetic fields: observations and models. Phys Earth Planet Inter. 2011;187:92–108.
  • Manneville JB, Olson P. Banded convection in rotating fluid spheres and the circulation of the Jovian atmosphere. Icarus. 1996;122:242–250.
  • Chandrasekhar S. Hydrodynamic and hydromagnetic stability. Oxford: Oxford University Press; 1961.
  • Rayleigh L. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Phil Mag. 1916;32:529–546.
  • Julien K, Knobloch E. Strongly nonlinear convection cells in a rapidly rotating fluid layer: the tilted f-plane. J Fluid Mech. 1998;360:141–178.
  • Aurnou JM, Bertin V, Grannan AM, et al. Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns. J Fluid Mech. 2018;846:846–876.
  • Niiler PP, Bisshopp FE. On the influence of Coriolis forces on onset of thermal convection. J Fluid Mech. 1965;22:753–761.
  • Greenspan HP. The theory of rotating fluids. Cambridge: Cambridge University Press; 1968.
  • Pedlosky J. Geophysical fluid dynamics. 2nd ed. New York: Springer; 1987.
  • Proudman J. On the motion of solids in a liquid possessing vorticity. Proc R Soc Lond A. 1916;92:408–424.
  • Taylor GI. Experiments on the motion of solid bodies in rotating fluids. Proc R Soc Lond A. 1923;104:213–218.
  • Sprague M, Julien K, Knobloch E, et al. Numerical simulation of an asymptotically reduced system for rotationally constrained convection. J Fluid Mech. 2006;551:141–174.
  • Julien K, Knobloch E, Werne J. A new class of equations for rotationally constrained flows. Theor Comput Fluid Dyn. 1998;11:251–261.
  • Julien K, Knobloch E, Milliff R, et al. Generalized quasi-geostrophy for spatially anistropic rotationally constrained flows. J Fluid Mech. 2006;555:233–274.
  • Julien K, Rubio AM, Grooms I, et al. Statistical and physical balances in low Rossby number Rayleigh–Bénard convection. Geophys Astrophys Fluid Dyn. 2012;106:392–428.
  • Ahlers G, Grossmann S, Lohse D. Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev Mod Phys. 2009;81:503–537.
  • Stevens RJAM, Clercx HJH, Lohse D. Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection. New J Phys. 2010;12:075005.
  • Yang Y, Verzicco R, Lohse D, et al. What rotation rate maximizes heat transport in rotating Rayleigh–Bénard convection with Prandtl number larger than one?. Phys Rev Fluids. 2020;5:053501.
  • Chong KL, Yang Y, Huang SD, et al. Confined Rayleigh–Bénard, rotating Rayleigh–Bénard, and double diffusive convection: a unifying view on turbulent transport enhancement through coherent structure manipulation. Phys Rev Lett. 2017;119:064501.
  • Rossby HT. A study of Bénard convection with and without rotation. J Fluid Mech. 1969;36:309–335.
  • Liu Y, Ecke RE. Heat transport scaling in turbulent Rayleigh–Bénard convection: effects of rotation and Prandtl number. Phys Rev Lett. 1997;79:2257–2260.
  • Kunnen RPJ, Clercx HJH, Geurts BJ. Breakdown of large-scale circulation in turbulent rotating convection. Europhys Lett. 2008;84:24001.
  • Zhong JQ, Stevens RJAM, Clercx HJH, et al. Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh–Bénard convection. Phys Rev Lett. 2009;102:044502.
  • Schmitz S, Tilgner A. Transitions in turbulent rotating Rayleigh–Bénard convection. Geophys Astrophys Fluid Dyn. 2010;104:481–489.
  • Zhong JQ, Ahlers G. Heat transport and the large-scale circulation in rotating turbulent Rayleigh–Bénard convection. J Fluid Mech. 2010;665:300–333.
  • Weiss S, Wei P, Ahlers G. Heat-transport enhancement in rotating turbulent Rayleigh–Bénard convection. Phys Rev E. 2016;93:043102.
  • Niemela JJ, Babuin S, Sreenivasan KR. Turbulent rotating convection at high Rayleigh and Taylor numbers. J Fluid Mech. 2010;649:509–522.
  • Ecke RE, Niemela JJ. Heat transport in the geostrophic regime of rotating Rayleigh–Bénard convection. Phys Rev Lett. 2014;113:114301.
  • Cheng JS, Stellmach S, Ribeiro A, et al. Laboratory-numerical models of rapidly rotating convection in planetary cores. Geophys J Int. 2015;201:1–17.
  • Cheng JS, Aurnou JM. Tests of diffusion-free scaling behaviors in numerical dynamo datasets. Earth Planet Sci Lett. 2016;436:121–129.
  • Stevens RJAM, Zhong JQ, Clercx HJH, et al. Transitions between turbulent states in rotating Rayleigh–Bénard convection. Phys Rev Lett. 2009;103:024503.
  • Kunnen RPJ, Stevens RJAM, Overkamp J, et al. The role of Stewartson and Ekman layers in turbulent rotating Rayleigh–Bénard convection. J Fluid Mech. 2011;688:422–442.
  • Cheng JS, Madonia M, Aguirre Guzmán AJ, et al. Laboratory exploration of heat transfer regimes in rapidly rotating turbulent convection. Phys Rev Fluids. 2020;5:113501.
  • Kunnen RPJ, Geurts BJ, Clercx HJH. Experimental and numerical investigation of turbulent convection in a rotating cylinder. J Fluid Mech. 2010;642:445–476.
  • Weiss S, Ahlers G. The large-scale flow structure in turbulent rotating Rayleigh–Bénard convection. J Fluid Mech. 2011;688:461–492.
  • Stevens RJAM, Clercx HJH, Lohse D. Heat transport and flow structure in rotating Rayleigh–Bénard convection. Eur J Mech B/Fluids. 2013;40:41–49.
  • King EM, Stellmach S, Buffett B. Scaling behaviour in Rayleigh–Bénard convection with and without rotation. J Fluid Mech. 2013;717:449–471.
  • Joshi P, Rajaei H, Kunnen RPJ, et al. Effect of particle injection on heat transfer in rotating Rayleigh–Bénard convection. Phys Rev Fluids. 2016;1:084301.
  • Julien K, Legg S, McWilliams J, et al. Rapidly rotating turbulent Rayleigh–Bénard convection. J Fluid Mech. 1996;322:243–273.
  • Weiss S, Stevens RJAM, Zhong JQ, et al. Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh–Bénard convection. Phys Rev Lett. 2010;105:224501.
  • Wei P, Weiss S, Ahlers G. Multiple transitions in rotating turbulent Rayleigh–Bénard convection. Phys Rev Lett. 2015;114:114506.
  • Rajaei H, Joshi P, Alards KMJ, et al. Transitions in turbulent rotating convection: a Lagrangian perspective. Phys Rev E. 2016;93:043129.
  • Alards KMJ, Kunnen RPJ, Stevens RJAM, et al. Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number. Phys Rev Fluids. 2019;4:074601.
  • Kunnen RPJ, Clercx HJH, Geurts BJ. Heat flux intensification by vortical flow localization in rotating convection. Phys Rev E. 2006;74:056306.
  • Zhang K, Liao X. The onset of convection in rotating circular cylinders with experimental boundary conditions. J Fluid Mech. 2009;622:63–73.
  • Zhong F, Ecke RE, Steinberg V. Asymmetric modes and the transition to vortex structures in rotating Rayleigh–Bénard convection. Phys Rev Lett. 1991;67:2473–2476.
  • Goldstein HF, Knobloch E, Mercader I, et al. Convection in a rotating cylinder: part 1. Linear theory for moderate Prandtl numbers. J Fluid Mech. 1993;248:583–604.
  • Zhong F, Ecke RE, Steinberg V. Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states. J Fluid Mech. 1993;249:135–159.
  • Herrmann J, Busse FH. Asymptotic theory of wall-attached convection in a rotating fluid layer. J Fluid Mech. 1993;255:183–194.
  • Goldstein HF, Knobloch E, Mercader I, et al. Convection in a rotating cylinder: part 2. Linear theory for low Prandtl numbers. J Fluid Mech. 1994;262:293–324.
  • Zhang K, Liao X, Busse FH. Asymptotic theory of inertial convection in a rotating cylinder. J Fluid Mech. 2007;575:449–471.
  • Horn S, Schmid PJ. Prograde, retrograde, and oscillatory modes in rotating Rayleigh–Bénard convection. J Fluid Mech. 2017;831:182–211.
  • Favier B, Knobloch E. Robust wall states in rapidly rotating Rayleigh–Bénard convection. J Fluid Mech. 2020;895:R2245.
  • Nieves D, Rubio AM, Julien K. Statistical classification of flow morphology in rapidly rotating Rayleigh–Bénard convection. Phys Fluids. 2014;26:086602.
  • Plumley M, Julien K, Marti P, et al. The effects of Ekman pumping on quasi-geostrophic Rayleigh–Bénard convection. J Fluid Mech. 2016;803:51–71.
  • Sakai S. The horizontal scale of rotating convection in the geostrophic regime. J Fluid Mech. 1997;333:85–95.
  • Kunnen RPJ, Clercx HJH, Geurts BJ. Vortex statistics in turbulent rotating convection. Phys Rev E. 2010;82:036306.
  • Grooms I, Julien K, Weiss JB, et al. Model of convective Taylor columns in rotating Rayleigh–Bénard convection. Phys Rev Lett. 2010;104:224501.
  • King EM, Aurnou JM. Thermal evidence for Taylor columns in turbulent rotating Rayleigh–Bénard convection. Phys Rev E. 2012;85:016313.
  • Rajaei H, Kunnen RPJ, Clercx HJH. Exploring the geostrophic regime of rapidly rotating convection with experiments. Phys Fluids. 2017;29:045105.
  • Noto D, Tasaka Y, Yanagisawa T, et al. Horizontal diffusive motion of columnar vortices in rotating Rayleigh–Bénard convection. J Fluid Mech. 2019;871:401–426.
  • Shi JQ, Lu HY, Ding SS, et al. Fine vortex structure and flow transition to the geostrophic regime in rotating Rayleigh–Bénard convection. Phys Rev Fluids. 2020;5:011501(R).
  • Chong KL, Shi JQ, Ding GY, et al. Vortices as Brownian particles in turbulent flows. Sci Adv. 2020;6:eaaz1110.
  • Rubio AM, Julien K, Knobloch E, et al. Upscale energy transfer in three-dimensional rapidly rotating turbulent convection. Phys Rev Lett. 2014;112:144501.
  • Favier B, Silvers LJ. Proctor MRE. inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection. Phys Fluids. 2014;26:096605.
  • Guervilly C, Hughes DW, Jones CA. Large-scale vortices in rapidly rotating Rayleigh–Bénard convection. J Fluid Mech. 2014;758:407–435.
  • Stellmach S, Lischper M, Julien K, et al. Approaching the asymptotic regime of rapidly rotating convection: boundary layers versus interior dynamics. Phys Rev Lett. 2014;113:254501.
  • Kunnen RPJ, Ostilla-Mónico R, van der Poel EP, et al. Transition to geostrophic convection: the role of the boundary conditions. J Fluid Mech. 2016;799:413–432.
  • Aguirre Guzmán AJ, Madonia M, Cheng JS, et al. Competition between Ekman plumes and vortex condensates in rapidly rotating thermal convection. Phys Rev Lett. 2020;125:214501.
  • Julien K, Aurnou JM, Calkins MA, et al. A nonlinear model for rotationally constrained convection with Ekman pumping. J Fluid Mech. 2016;798:50–87.
  • Boubnov BM, Golitsyn GS. Experimental study of convective structures in rotating fluids. J Fluid Mech. 1986;167:503–531.
  • Boubnov BM, Golitsyn GS. Temperature and velocity field regimes of convective motions in a rotating plane fluid layer. J Fluid Mech. 1990;219:215–239.
  • Fernando HJS, Chen RR, Boyer DL. Effects of rotation on convective turbulence. J Fluid Mech. 1991;228:513–547.
  • Vorobieff P, Ecke RE. Turbulent rotating convection: an experimental study. J Fluid Mech. 2002;458:191–218.
  • Cheng JS, Aurnou JM, Julien K, et al. A heuristic framework for next-generation models of geostrophic convective turbulence. Geophys Astrophys Fluid Dyn. 2018;112:277–300.
  • de Wit XM, Aguirre Guzmán AJ, Madonia M, et al. Turbulent rotating convection confined in a slender cylinder: the sidewall circulation. Phys Rev Fluids. 2020;5:023502.
  • Zhang X, van Gils DPM, Horn S, et al. Boundary zonal flow in rotating turbulent Rayleigh–Bénard convection. Phys Rev Lett. 2020;124:084505.
  • Shishkina O. Tenacious wall states in thermal convection in rapidly rotating containers. J Fluid Mech. 2020;898:4091.
  • Lu HY, Ding GY, Shi JQ. Heat transport scaling and transition in geostrophic rotating convection with varying aspect ratio. 2020. ArXiv:2007.13279
  • Horn S, Shishkina O. Toroidal and poloidal energy in rotating Rayleigh–Bénard convection. J Fluid Mech. 2015;762:232–255.
  • Julien K, Knobloch E, Rubio AM, et al. Heat transport in low-Rossby-number Rayleigh–Bénard convection. Phys Rev Lett. 2012;109:254503.
  • Plumley M, Julien K, Marti P, et al. Sensitivity of rapidly rotating Rayleigh–Bénard convection to Ekman pumping. Phys Rev Fluids. 2017;2:094801.
  • King EM, Stellmach S, Aurnou JM. Heat transfer by rapidly rotating Rayleigh–Bénard convection. J Fluid Mech. 2012;691:568–582.
  • Liu Y, Ecke RE. Heat transport measurements in turbulent rotating Rayleigh–Bénard convection. Phys Rev E. 2009;80:036314.
  • King EM, Stellmach S, Noir J, et al. Boundary layer control of rotating convection systems. Nature. 2009;457:301–304.
  • Weiss S, Ahlers G. Heat transport by turbulent rotating Rayleigh–Bénard convection and its dependence on the aspect ratio. J Fluid Mech. 2011;684:407–426.
  • Kunnen RPJ, Clercx HJH, Geurts BJ. Enhanced vertical inhomogeneity in turbulent rotating convection. Phys Rev Lett. 2008;101:174501.
  • Rajaei H, Alards KMJ, Kunnen RPJ, et al. Velocity and acceleration statistics in rapidly rotating Rayleigh–Bénard convection. J Fluid Mech. 2018;857:374–397.
  • Stevens RJAM, Overkamp J, Lohse D, et al. Effect of aspect ratio on vortex distribution and heat transfer in rotating Rayleigh–Bénard convection. Phys Rev E. 2011;84:056313.
  • Horn S, Shishkina O. Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water. Phys Fluids. 2014;26:055111.
  • Kunnen RPJ, Corre Y, Clercx HJH. Vortex plume distribution in confined turbulent rotating convection. EPL. 2013;104:54002.
  • Malkus WVR. The heat transport and spectrum of thermal turbulence. Proc R Soc Lond A. 1954;225:196–212.
  • Nikolaenko A, Brown E, Funfschilling D, et al. Heat transport by turbulent Rayleigh–Bénard convection in cylindrical cells with aspect ratio one and less. J Fluid Mech. 2005;523:251–260.
  • Funfschilling D, Brown E, Nikolaenko A, et al. Heat transport by turbulent Rayleigh–Bénard convection in cylindrical samples with aspect ratio one and larger. J Fluid Mech. 2005;536:145–154.
  • Kraichnan RH. Turbulent thermal convection at arbitrary Prandtl number. Phys Fluids. 1962;5:1374–1389.
  • Spiegel EA. Convection in stars: I. Basic Boussinesq convection. Annu Rev Astron Astrophys. 1971;9:323–352.
  • Iyer KP, Scheel JD, Schumacher J, et al. Classical 1/3 scaling of convection holds up to Ra=1015. Proc Natl Acad Sci USA. 2020;117:7594–7598.
  • Chavanne X, Chillá F, Castaing B, et al. Observation of the ultimate regime in Rayleigh–Bénard convection. Phys Rev Lett. 1997;79:3648–3651.
  • He X, Funfschilling D, Nobach H, et al. Transition to the ultimate state of turbulent Rayleigh–Bénard convection. Phys Rev Lett. 2012;108:024502.
  • Schmitz S, Tilgner A. Heat transport in rotating convection without Ekman layers. Phys Rev E. 2009;80:015305(R).
  • Maffei S, Krouss MJ, Julien. On the inverse cascade and flow speed scaling behavior in rapidly rotating Rayleigh–Bénard convection. 2020. ArXiv:2003.01669
  • Frisch U. Turbulence: the legacy of A. N. Kolmogorov. Cambridge: Cambridge University Press; 1995.
  • Pope SB. Turbulent flows. Cambridge: Cambridge University Press; 2000.
  • Boffetta G, Ecke RE. Two-dimensional turbulence. Annu Rev Fluid Mech. 2011;44:427–451.
  • Alexakis A, Biferale L. Cascades and transitions in turbulent flows. Phys Rep. 2018;767–769:1–101.
  • Guervilly C, Hughes DW. Jets and large-scale vortices in rotating Rayleigh–Bénard convection. Phys Rev Fluids. 2017;2:113503.
  • Julien K, Knobloch E, Plumley M. Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection. J Fluid Mech. 2018;837:R4.
  • Favier B, Guervilly C, Knobloch E. Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection. J Fluid Mech. 2019;864:R1.
  • Homsy GM, Hudson JL. Centrifugal convection and its effect on the asymptotic stability of a bounded rotating fluid heated from below. J Fluid Mech. 1971;48:605–624.
  • Horn S, Aurnou JM. Regimes of Coriolis-centrifugal convection. Phys Rev Lett. 2018;120:204502.
  • Horn S, Aurnou JM. Rotating convection with centrifugal buoyancy: numerical predictions for laboratory experiments. Phys Rev Fluids. 2019;4:073501.
  • Hart JE, Ohlsen DR. On the thermal offset in turbulent rotating convection. Phys Fluids. 1999;11:2101–2107.
  • Kunnen RPJ, Clercx HJH, van Heijst GJF. The structure of sidewall boundary layers in confined rotating Rayleigh–Bénard convection. J Fluid Mech. 2013;727:509–532.
  • Oberbeck A. Über die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperaturdifferenzen. Ann Phys. 1879;243:271–292.
  • Boussinesq J. Théorie analytique de la chaleur. Paris: Gauthier-Villars; 1903.
  • Ahlers G, Brown E, Fontenele Araujo F, et al. Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection. J Fluid Mech. 2006;569:409–445.
  • Wu XZ, Libchaber A. Non-Boussinesq effects in free thermal convection. Phys Rev A. 1991;43:2833–2839.
  • Batchelor GK. An introduction to fluid dynamics. Cambridge: Cambridge University Press; 1967.
  • Liao X, Zhang K. On flow in weakly precessing cylinders: the general asymptotic solution. J Fluid Mech. 2012;709:610–621.
  • Meunier P, Eloy C, Lagrange R, et al. A rotating fluid cylinder subject to weak precession. J Fluid Mech. 2008;599:405–440.