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Vortex dynamics in rotating Rayleigh–Bénard convection

Published online by Cambridge University Press:  06 November 2023

Shan-Shan Ding Open the ORCID record for Shan-Shan Ding [Opens in a new window] ,
Guang-Yu Ding Open the ORCID record for Guang-Yu Ding [Opens in a new window] ,
Kai Leong Chong Open the ORCID record for Kai Leong Chong [Opens in a new window] ,
Wen-Tao Wu ,
Ke-Qing Xia Open the ORCID record for Ke-Qing Xia [Opens in a new window]  and
Jin-Qiang Zhong Open the ORCID record for Jin-Qiang Zhong [Opens in a new window]
Shan-Shan Ding
Affiliation:
School of Physics Science and Engineering, Tongji University, Shanghai 200092, PR China
Guang-Yu Ding
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, PR China
Kai Leong Chong
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, PR China Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Wen-Tao Wu
Affiliation:
School of Physics Science and Engineering, Tongji University, Shanghai 200092, PR China
Ke-Qing Xia*
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, PR China
Jin-Qiang Zhong*
Affiliation:
School of Physics Science and Engineering, Tongji University, Shanghai 200092, PR China Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, PR China
*
†Email addresses for correspondence: xiakq@sustech.edu.cn, jinqiang@fudan.edu.cn
†Email addresses for correspondence: xiakq@sustech.edu.cn, jinqiang@fudan.edu.cn
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Abstract

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$. Under slow rotations ($Ra\approx 80\,Ra_{c}$), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$. The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ($4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$, and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ($1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices.

JFM classification

Turbulent Flows: Turbulent convection Geophysical and Geological Flows: Rotating flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 974 , 10 November 2023 , A43
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Aurnou, J.M., Bertin, V. & Grannan, A.M. 2018 Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns. J. Fluid Mech. 846, 846–876.CrossRefGoogle Scholar
Boubnov, B.M. & Golitsyn, G.S. 1986 Experimental study of convective structures in rotating fluids. J. Fluid Mech. 167, 503–531.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Chen, X., Dong, X., Be'er, A., Swinney, H.L. & Zhang, H.P. 2012 Scale-invariant correlations in dynamic bacterial clusters. Phys. Rev. Lett. 108 (14), 148101.CrossRefGoogle ScholarPubMed
Chong, K.L., Ding, G. & Xia, K.-Q. 2018 Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence. J. Comput. Phys. 375, 1045–1058.CrossRefGoogle Scholar
Chong, K.L., Shi, J.-Q., Ding, S.-S., Ding, G.-Y., Lu, H.-Y., Zhong, J.-Q. & Xia, K.-Q. 2020 Vortices as Brownian particles in turbulent flows. Sci. Adv. 6, eaaz1110.CrossRefGoogle ScholarPubMed
Ding, S.-S., Chong, K.L., Shi, J.-Q., Ding, G.-Y., Lu, H.-Y., Xia, K.-Q. & Zhong, J.-Q. 2021 Inverse centrifugal effect induced by collective motion of vortices in rotating turbulent convection. Nat. Commun. 12, 5585.CrossRefGoogle Scholar
Ding, S.-S., Zhang, H.-L., Chen, D.-T. & Zhong, J.-Q. 2022 Vortex patterns in rapidly rotating Rayleigh–Bénard convection under spatial periodic forcing. J. Fluid Mech. 950, R1.CrossRefGoogle Scholar
Ferenc, J.-S. & Néda, Z. 2007 On the size distribution of Poisson Voronoi cells. Physica A 385 (2), 518–526.CrossRefGoogle Scholar
Fernando, H.J.S. & Smith, D.C. 2001 Vortex structures in geophysical convection. Eur. J. Mech. B/Fluids 20, 437–470.CrossRefGoogle Scholar
Fujita, K., Tasaka, Y., Yanagisawa, T., Noto, D. & Murai, Y. 2020 Three-dimensional visualization of columnar vortices in rotating Rayleigh–Bénard convection. J. Vis. 24, 635–647.CrossRefGoogle Scholar
Gascard, J.-C., Watson, A.J., Messias, M.-J., Olsson, K.A., Johannessen, T. & Simonsen, K. 2002 Long-lived vortices as a mode of deep ventilation in the Greenland Sea. Nature 416, 525–527.CrossRefGoogle ScholarPubMed
Gavriel, N. & Kaspi, Y. 2021 The number and location of Jupiter's circumpolar cyclones explained by vorticity dynamics. Nat. Geosci. 14, 559–563.CrossRefGoogle Scholar
Gavriel, N. & Kaspi, Y. 2022 The oscillatory motion of Jupiter's polar cyclones results from vorticity dynamics. Geophys. Res. Lett. 49, e2022GL098708.CrossRefGoogle Scholar
Grooms, I., Julien, K., Weiss, J.B. & Knobloch, E. 2010 Model of convective Taylor columns in rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 104, 224501.CrossRefGoogle ScholarPubMed
Hart, J.E. & Olsen, D.R. 1999 On the thermal offset in turbulent rotating convection. Phys. Fluids 11, 2101–2107.CrossRefGoogle Scholar
Hopfinger, E.J. & van Heijst, G.J.F. 1993 Vortices in rotating fluids. Annu. Rev. Fluid Mech. 25, 241–289.CrossRefGoogle Scholar
Horn, S. & Aurnou, J.M. 2019 Rotating convection with centrifugal buoyancy: numerical predictions for laboratory experiments. Phys. Rev. Fluids 4, 073501.CrossRefGoogle Scholar
Hu, Y.-B., Huang, S.-D., Xie, Y.-C. & Xia, K.-Q. 2021 Centrifugal-force-induced flow bifurcations in turbulent thermal convection. Phys. Rev. Lett. 127, 244501.CrossRefGoogle ScholarPubMed
Jones, C.A. 2011 Planetary magnetic fields and fluid dynamos. Annu. Rev. Fluid Mech. 43, 583–614.CrossRefGoogle Scholar
Julien, K. & Knobloch, E. 1998 Strongly nonlinear convection cells in a rapidly rotating fluid layer: the tilted $f$-plane. J. Fluid Mech. 360, 141–178.CrossRefGoogle Scholar
Julien, K., Legg, S., McWilliams, J. & Werne, J. 1996 Rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 322, 243–273.CrossRefGoogle 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.CrossRefGoogle Scholar
Kaczorowski, M. & Xia, K.-Q. 2013 Turbulent flow in the bulk of Rayleigh–Bénard convection: small-scale properties in a cubic cell. J. Fluid Mech. 722, 596–617.CrossRefGoogle Scholar
King, E.M. & Aurnou, J.M. 2012 Thermal evidence for Taylor columns in turbulent rotating Rayleigh–Bénard convection. Phys. Rev. E 85, 016313.CrossRefGoogle ScholarPubMed
King, E.M., Stellmach, S., Noir, J., Hansen, U. & Aurnou, J.M. 2009 Boundary layer control of rotating convection systems. Nature 457, 301.CrossRefGoogle ScholarPubMed
Kundu, P.K. & Cohen, I.M. 2008 Fluid Mechanics. Academic Press.Google Scholar
Kunnen, R.P.J. 2021 The geostrophic regime of rapidly rotating turbulent convection. J. Turbul. 22 (4–5), 267–296.CrossRefGoogle Scholar
Kunnen, R.P.J., Clercx, H.J.H. & Geurts, B.J. 2010 Vortex statistics in turbulent rotating convection. Phys. Rev. E 82, 036306.CrossRefGoogle ScholarPubMed
Li, C., Ingersoll, A.P., Klipfel, A.P. & Brettle, H. 2020 Modeling the stability of polygonal patterns of vortices at the poles of Jupiter as revealed by the Juno spacecraft. Proc. Natl Acad. Sci. USA 117, 24082–24087.CrossRefGoogle ScholarPubMed
Liu, Y. & Ecke, R.E. 2011 Local temperature measurements in turbulent rotating Rayleigh–Bénard convection. Phys. Rev. E 84, 016311.CrossRefGoogle ScholarPubMed
Lu, H.-Y., Ding, G.-Y., Shi, J.-Q., Xia, K.-Q. & Zhong, J.-Q. 2021 Heat-transport scaling and transition in geostrophic rotating convection with varying aspect ratio. Phys. Rev. Fluids 6 (7), L071501.CrossRefGoogle Scholar
Marshall, J. & Scott, F. 1999 Open-ocean convection: observations, theory, and models. Rev. Geophys. 37, 1–64.CrossRefGoogle Scholar
Mura, A., et al. 2021 Oscillations and stability of the Jupiter polar cyclones. Geophys. Res. Lett. 48, e2021GL094235.CrossRefGoogle Scholar
Nieves, D., Rubio, A.M. & Julien, K. 2014 Statistical classification of flow morphology in rapidly rotating Rayleigh–Bénard convection. Phys. Fluids 26, 086602.CrossRefGoogle Scholar
Niiler, P.P. & Bisshopp, F.E. 1965 On the influence of Coriolis force on onset of thermal convection. J. Fluid Mech. 22, 753–761.CrossRefGoogle Scholar
Noto, D., Tasaka, Y., Yanagisawa, T. & Murai, Y. 2019 Horizontal diffusive motion of columnar vortices in rotating Rayleigh–Bénard convection. J. Fluid Mech. 871, 401.CrossRefGoogle Scholar
Portegies, J.W., Kunnen, R.P.J., van Heijst, G.J.F. & Molenaar, J. 2008 A model for vortical plumes in rotating convection. Phys. Fluids 20, 066602.CrossRefGoogle Scholar
Rajaei, H., Kunnen, R.P.J. & Clercx, H.J.H. 2017 Exploring the geostrophic regime of rapidly rotating convection with experiments. Phys. Fluids 20, 045105.CrossRefGoogle Scholar
Sakai, S. 1997 The horizontal scale of rotating convection in the geostrophic regime. J. Fluid Mech. 333, 85–95.CrossRefGoogle Scholar
Schecter, D.A. & Dubin, D.H. 1999 Vortex motion driven by a background vorticity gradient. Phys. Rev. Lett. 83, 2191–2194.CrossRefGoogle Scholar
Shi, J.-Q., Lu, H.-Y., Ding, S.-S. & Zhong, J.-Q. 2020 Fine vortex structure and flow transition to the geostrophic regime in rotating Rayleigh–Bénard convection. Phys. Rev. Fluids 5, 011501(R).CrossRefGoogle Scholar
Sprague, M., Julien, K., Knobloch, E. & Werne, J. 2006 Numerical simulation of an asymptotically reduced system for rotationally constrained convection. J. Fluid Mech. 551, 141–174.CrossRefGoogle Scholar
Stellmach, S., Lischper, M., Julien, K., Vasil, G., Cheng, J.S., Ribeiro, A., King, E.M. & Aurnou, J.M. 2014 Approaching the asymptotic regime of rapidly rotating convection: boundary layers versus interior dynamics. Phys. Rev. Lett. 113, 254501.CrossRefGoogle ScholarPubMed
Tagawa, Y., Mercado, J.M., Prakash, V.N., Calzavarini, E., Sun, C. & Lohse, D. 2012 Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence. J. Fluid Mech. 693, 201–215.CrossRefGoogle Scholar
Vallis, G.K. 2006 Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Vorobieff, P. & Ecke, R.E. 1998 Vortex structure in rotating Rayleigh–Bénard convection. J. Fluid Mech. 123, 156–160.Google Scholar
Vorobieff, P. & Ecke, R.E. 2002 Turbulent rotating convection: an experimental study. J. Fluid Mech. 458, 191–218.CrossRefGoogle Scholar
Westerweel, J., Elsinga, G.E. & Adrian, R.J. 2013 Particle image velocimetry for complex and turbulent flows. Annu. Rev. Fluid Mech. 45, 409–436.CrossRefGoogle Scholar
de Wit, X.M., Aguirre Guzmán, A.J., Madonia, M., Cheng, J.S., Clercx, H.J.H. & Kunnen, R.P.J. 2020 Turbulent rotating convection confined in a slender cylinder: the sidewall circulation. Phys. Rev. Fluids 5, 023502.CrossRefGoogle Scholar
Zhang, X., van Gils, D.P.M., Horn, S., Wedi, M., Zwirner, L., Ahlers, G., Ecke, R.E., Weiss, S., Bodenschatz, E. & Shishkina, O. 2020 Boundary zonal flow in rotating turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 124, 084505.CrossRefGoogle ScholarPubMed
Zhong, F., Ecke, R. & Steinberg, V. 1993 Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states. J. Fluid Mech. 249, 135.CrossRefGoogle Scholar