Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-16T12:32:29.943Z Has data issue: false hasContentIssue false

Velocity and acceleration statistics in rapidly rotating Rayleigh–Bénard convection

Published online by Cambridge University Press:  22 October 2018

Hadi Rajaei*
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Kim M. J. Alards
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Rudie P. J. Kunnen
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Herman J. H. Clercx
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
*
Email address for correspondence: hadi_rajaei@yahoo.com

Abstract

Background rotation causes different flow structures and heat transfer efficiencies in Rayleigh–Bénard convection. Three main regimes are known: rotation unaffected, rotation affected and rotation dominated. It has been shown that the transition between rotation-unaffected and rotation-affected regimes is driven by the boundary layers. However, the physics behind the transition between rotation-affected and rotation-dominated regimes are still unresolved. In this study, we employ the experimentally obtained Lagrangian velocity and acceleration statistics of neutrally buoyant immersed particles to study the rotation-affected and rotation-dominated regimes and the transition between them. We have found that the transition to the rotation-dominated regime coincides with three phenomena; suppressed vertical motions, strong penetration of vortical plumes deep into the bulk and reduced interaction of vortical plumes with their surroundings. The first two phenomena are used as confirmations for the available hypotheses on the transition to the rotation-dominated regime while the last phenomenon is a new argument to describe the regime transition. These findings allow us to better understand the rotation-dominated regime and the transition to this regime.

Type
JFM Papers
Copyright
© 2018 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.)

References

Agrawal, B. N. 1993 Dynamic characteristics of liquid motion in partially filled tanks of a spinning spacecraft. J. Guid. Control Dyn. 16, 636640.Google Scholar
Alards, K. M. J., Rajaei, H., Del Castello, L., Kunnen, R. P. J., Toschi, F. & Clercx, H. J. H. 2017 Geometry of tracer trajectories in rotating turbulent flows. Phys. Rev. Fluids 2, 044601.Google Scholar
Boubnov, B. M. & Golitsyn, G. S. 1986 Experimental study of convective structures in rotating fluids. J. Fluid Mech. 167, 503531.Google Scholar
Busse, F. H. 2010 Mean zonal flows generated by librations of a rotating spherical cavity. J. Fluid Mech. 650, 505512.Google Scholar
Chan, S.-K. 1974 Investigation of turbulent convection under a rotational constraint. J. Fluid Mech. 64, 477506.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Cheng, J. S., Stellmach, S., Ribeiro, A., Grannan, A., King, E. M. & Aurnou, J. M. 2015 Laboratory-numerical models of rapidly rotating convection in planetary cores. Geophys. J. Intl 201, 117.Google Scholar
Constantin, P., Hallstrom, C. & Putkaradze, V. 1999 Heat transport in rotating convection. Physica D 125, 275284.Google Scholar
Del Castello, L. & Clercx, H. J. H. 2011 Lagrangian velocity autocorrelations in statistically steady rotating turbulence. Phys. Rev. E 83, 056316.Google Scholar
Doering, C. R. & Constantin, P. 2001 On upper bounds for infinite Prandtl number convection with or without rotation. J. Maths Phys. 42, 784795.Google Scholar
Ecke, R. E. & Niemela, J. J. 2014 Heat transport in the geostrophic regime of rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 113, 114301.Google Scholar
Gans, R. F. 1970 On the precession of a resonant cylinder. J. Fluid Mech. 41, 865872.Google Scholar
Gervais, P., Baudet, C. & Gagne, Y. 2007 Acoustic Lagrangian velocity measurement in a turbulent air jet. Exp. Fluids 42, 371384.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google 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.Google Scholar
Hart, J. E. & Kittelman, S. 1996 Instabilities of the sidewall boundary layer in a differentially driven rotating cylinder. Phys. Fluids 8, 692696.Google Scholar
Horn, S. & Aurnou, J. M. 2018 Regimes of Coriolis-centrifugal convection. Phys. Rev. Lett. 120 (20), 204502.Google Scholar
Horn, S. & Shishkina, O. 2015 Toroidal and poloidal energy in rotating Rayleigh–Bénard convection. J. Fluid Mech. 762, 232255.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, streams, and convergence zones in turbulent flows. Report CTR-S88, Center for Turbulence Research.Google Scholar
Joshi, P., Rajaei, H., Kunnen, R. P. J. & Clercx, H. J. H. 2016 Effect of particle injection on heat transfer in rotating Rayleigh–Bénard convection. Phys. Rev. Fluids 1 (8), 084301.Google Scholar
Julien, K., Knobloch, E., Rubio, A. M. & Vasil, G. M. 2012a Heat transport in low-Rossby-number Rayleigh–Bénard convection. Phys. Rev. Lett. 109, 254503.Google Scholar
Julien, K., Legg, S., McWlliams, J. & Werne, J. 1996 Rapidly rotating turbulent Rayleigh–Bénard convection. J. Fluid Mech. 322, 243273.Google Scholar
Julien, K., Rubio, A. M., Grooms, I. & Knobloch, E. 2012b Statistical and physical balances in low Rossby number Rayleigh–Bénard convection. Geophys. Astrophys. Fluid Dyn. 106, 392428.Google Scholar
King, E. M., Stellmach, S. & Aurnou, J. M. 2012 Heat transfer by rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 691, 568582.Google Scholar
King, E. M., Stellmach, S., Noir, J., Hansen, U. & Aurnou, J. M. 2009 Boundary layer control of rotating convection systems. Nature 457, 301304.Google Scholar
Kobine, J. J. 1995 Inertial wave dynamics in a rotating and precessing cylinder. J. Fluid Mech. 303, 233252.Google Scholar
Kunnen, R. P. J., Clercx, H. J. H. & Geurts, B. J. 2006 Heat flux intensification by vortical flow localization in rotating convection. Phys. Rev. E 74, 056306.Google Scholar
Kunnen, R. P. J., Clercx, H. J. H. & Geurts, B. J. 2008 Enhanced vertical inhomogeneity in turbulent rotating convection. Phys. Rev. Lett. 101, 174501.Google Scholar
Kunnen, R. P. J., Corre, Y. & Clercx, H. J. H. 2014 Vortex plume distribution in confined turbulent rotating convection. Europhys. Lett. 104, 54002.Google Scholar
Kunnen, R. P. J., Geurts, B. J. & Clercx, H. J. H. 2010 Experimental and numerical investigation of turbulent convection in a rotating cylinder. J. Fluid Mech. 642, 445476.Google Scholar
Kunnen, R. P. J., Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R. & Lohse, D. 2016 Transition to geostrophic convection: the role of the boundary conditions. J. Fluid Mech. 799, 413432.Google Scholar
Kunnen, R. P. J., Stevens, R. J. A. M., Overkamp, J., Sun, C., van Heijst, G. J. F. & Clercx, H. J. H. 2011 The role of Stewartson and Ekman layers in turbulent rotating Rayleigh–Bénard convection. J. Fluid Mech. 688, 422442.Google Scholar
Le Bars, M., Cébron, D. & Le Gal, P. 2015 Flows driven by libration, precession, and tides. Annu. Rev. Fluid Mech. 47, 163193.Google Scholar
Liao, X. & Zhang, K. 2012 On flow in weakly precessing cylinders: the general asymptotic solution. J. Fluid Mech. 709, 610621.Google Scholar
Liu, Y. & Ecke, R. E. 1997 Heat transport scaling in turbulent Rayleigh–Bénard convection: effects of rotation and Prandtl number. Phys. Rev. Lett. 79, 2257.Google Scholar
Liu, Y. & Ecke, R. E. 2009 Heat transport measurements in turbulent rotating Rayleigh–Bénard convection. Phys. Rev. E 80, 036314.Google Scholar
Lopez, J. M. & Marques, F. 2010 Sidewall boundary layer instabilities in a rapidly rotating cylinder driven by a differentially corotating lid. Phys. Fluids 22, 114109.Google Scholar
Lopez, J. M. & Marques, F. 2014 Rapidly rotating cylinder flow with an oscillating sidewall. Phys. Rev. E 89, 013013.Google Scholar
Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87118.Google Scholar
Maas, H. G., Gruen, A. & Papantoniou, D. 1993 Particle tracking velocimetry in three-dimensional flows. Part I. Photogrammetric determination of particle coordinates. Exp. Fluids 15, 133146.Google Scholar
Malik, N. A., Dracos, T. & Papantoniou, D. A. 1993 Particle tracking velocimetry in three-dimensional flows. Part II. Particle tracking. Exp. Fluids 15, 279294.Google Scholar
Manasseh, R. 1992 Breakdown regimes of inertia waves in a precessing cylinder. J. Fluid Mech. 243, 261296.Google Scholar
Meunier, P., Eloy, C., Lagrange, R. & Nadal, F. 2008 A rotating fluid cylinder subject to weak precession. J. Fluid Mech. 599, 405440.Google Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004a Experimental Lagrangian acceleration probability density function measurement. Physica D 193, 245251.Google Scholar
Mordant, N., Lévêque, E. & Pinton, J.-F. 2004b Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence. New J. Phys. 6, 116.Google Scholar
Mordant, N., Metz, P., Michel, O. & Pinton, J.-F. 2001 Measurement of Lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87, 214501.Google Scholar
Niemela, J. J., Babuin, S. & Sreenivasan, K. R. 2010 Turbulent rotating convection at high Rayleigh and Taylor numbers. J. Fluid Mech. 649, 509522.Google Scholar
Noir, J., Calkins, M. A., Lasbleis, M., Cantwell, J. & Aurnou, J. M. 2010 Experimental study of libration-driven zonal flows in a straight cylinder. Phys. Earth Planet. Inter. 182, 98106.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics, 2nd edn. Springer.Google 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.Google Scholar
Rajaei, H.2017 Rotating Rayleigh–Bénard convetion. PhD thesis, Eindhoven University of Technology.Google Scholar
Rajaei, H., Joshi, P., Alards, K. M. J., Kunnen, R. P. J., Toschi, F. & Clercx, H. J. H. 2016a Transitions in turbulent rotating convection: a Lagrangian perspective. Phys. Rev. E 93, 043129.Google Scholar
Rajaei, H., Joshi, P., Kunnen, R. P. J. & Clercx, H. J. H. 2016b Flow anisotropy in rotating buoyancy-driven turbulence. Phys. Rev. Fluids 1, 044403.Google Scholar
Rajaei, H., Kunnen, R. P. J. & Clercx, H. J. H. 2017 Exploring the geostrophic regime of rapidly rotating convection with experiments. Phys. Fluids 29, 045105.Google Scholar
Rossby, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309335.Google Scholar
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.Google Scholar
Sakai, S. 1997 The horizontal scale of rotating convection in the geostrophic regime. J. Fluid Mech. 333, 8595.Google Scholar
Sawford, B. L. 1991 Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids A 3, 15771586.Google Scholar
Schmitz, S. & Tilgner, A. 2009 Heat transport in rotating convection without Ekman layers. Phys. Rev. E 80, 015305.Google Scholar
Schmitz, S. & Tilgner, A. 2010 Transitions in turbulent rotating Rayleigh–Bénard convection. Geophys. Astrophys. Fluid Dyn. 104, 481489.Google Scholar
Song, H. & Tong, P. 2010 Scaling laws in turbulent Rayleigh–Bénard convection under different geometry. Europhys. Lett. 90, 44001.Google 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, 141174.Google 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.Google Scholar
Stevens, R. J. A. M., Clercx, H. J. H. & Lohse, D. 2010 Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection. New J. Phys. 12, 075005.Google Scholar
Stevens, R. J. A. M., Clercx, H. J. H. & Lohse, D. 2013 Heat transport and flow structure in rotating Rayleigh–Bénard convection. Eur. J. Mech. (B/Fluids) 40, 4149.Google Scholar
Stevens, R. J. A. M., Zhong, J.-Q., Clercx, H. J. H., Ahlers, G. & Lohse, D. 2009 Transitions between turbulent states in rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 103, 024503.Google Scholar
Stewartson, K. 1959 On the stability of a spinning top containing liquid. J. Fluid Mech. 5, 577592.Google Scholar
Sun, C., Zhou, Q. & Xia, K.-Q. 2006 Cascades of velocity and temperature fluctuations in buoyancy-driven thermal turbulence. Phys. Rev. Lett. 97, 144504.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. A 20, 196211.Google Scholar
Vanyo, J. P. 2015 Rotating Fluids in Engineering and Science. Elsevier.Google Scholar
Vitanov, N. K. 2003 Convective heat transport in a rotating fluid layer of infinite Prandtl number: optimum fields and upper bounds on Nusselt number. Phys. Rev. E 67, 026322.Google Scholar
Vorobieff, P. & Ecke, R. E. 2002 Turbulent rotating convection: an experimental study. J. Fluid Mech. 458, 191218.Google Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121160.Google Scholar
Weiss, S. & Ahlers, G. 2011a Heat transport by turbulent rotating Rayleigh–Bénard convection and its dependence on the aspect ratio. J. Fluid Mech. 684, 407426.Google Scholar
Weiss, S. & Ahlers, G. 2011b The large-scale flow structure in turbulent rotating Rayleigh–Bénard convection. J. Fluid Mech. 688, 461492.Google Scholar
Weiss, S., Stevens, R. J. A. M., Zhong, J.-Q., Clercx, H. J. H., Lohse, D. & Ahlers, G. 2010 Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 105, 224501.Google Scholar
Willneff, J. 2002 3D particle tracking velocimetry based on image and object space information. Intl Arch. Photogramm. Rem. Sens. Spatial Inform. Sci. 34, 601606.Google Scholar
Willneff, J.2003 A spatio-temporal matching algorithm for 3D particle tracking velocimetry. PhD thesis, Swiss Federal Institute of Technology, Zürich.Google Scholar
Wu, C.-C. & Roberts, P. H. 2009 On a dynamo driven by topographic precession. Geophys. Astrophys. Fluid Dyn. 103, 467501.Google Scholar
Zhong, F., Ecke, R. E. & Steinberg, V. 1993 Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states. J. Fluid Mech. 249, 135159.Google Scholar
Zhong, J.-Q. & Ahlers, G. 2010 Heat transport and the large-scale circulation in rotating turbulent Rayleigh–Bénard convection. J. Fluid Mech. 665, 300333.Google Scholar
Zhong, J.-Q., Stevens, R. J. A. M., Clercx, H. J. H., Verzicco, R., Lohse, D. & Ahlers, G. 2009 Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 102, 044502.Google Scholar