Skip to main content
SpringerLink
Log in

Transport Phenomena in Rotating Turbulence

  • Chapter
  • First Online:
Book cover Mixing and Dispersion in Flows Dominated by Rotation and Buoyancy

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 580))

  • 810 Accesses

Abstract

The role of rotation on turbulence and some of its transport properties will be reviewed with emphasis on two specific cases: statistically steady or decaying rotating turbulence and rotating thermally driven turbulence. For this purpose we briefly address a few basic concepts relevant for understanding processes in rotating (turbulent) flows such as the emergence of coherent structures, the Taylor-Proudman theorem, quasi-two-dimensional turbulence, inertial waves and Ekman boundary layers. The effect of rotation on turbulence will subsequently be illustrated with two sets of laboratory experiments: one with steadily forced rotating turbulence and another with rotating turbulent convection.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • G. Ahlers, S. Grossmann, D. Lohse, Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Modern Phys. 81, 503–537 (2009)

    Article  Google Scholar 

  • J. Bardina, J.H. Ferziger, R.S. Rogallo, Effect of rotation on isotropic turbulence: computation and modelling. J. Fluid Mech. 154, 321–336 (1985)

    Article  Google Scholar 

  • C.N. Baroud, B.B. Plapp, Z.-S. She, H.L. Swinney, Anomalous self-similarity in a turbulent rapidly rotating fluid. Phys. Rev. Lett. 88(11), 114501 (2002)

    Article  Google Scholar 

  • C.N. Baroud, B.B. Plapp, H.L. Swinney, Z.-S. She, Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows. Phys. Fluids 15(8), 2091–2104 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • P. Bartello, O. Métais, M. Lesieur, Coherent structures in rotating three-dimensional turbulence. J. Fluid Mech. 273, 1–29 (1994)

    Article  MathSciNet  Google Scholar 

  • G. Boffetta, R.E. Ecke, Two-dimensional turbulence. Ann. Rev. Fluid Mech. 44, 427–451 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  • G. Boffetta, S. Musacchio, Evidence for the double cascade scenario in two-dimensional turbulence. Phys. Rev. E 82(1), 016307 (2010)

    Article  Google Scholar 

  • C. Cambon, N.N. Mansour, F.S. Godeferd, Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303–332 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • A. Campagne, B. Gallet, F. Moisy, P.-P. Cortet, Direct and inverse energy cascades in a forced rotating turbulence experiment. Phys. Fluids 26(12), 125112 (2014)

    Article  Google Scholar 

  • S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961)

    MATH  Google Scholar 

  • H.J.H. Clercx, G.J.F. van Heijst, Two-dimensional Navier-Stokes turbulence in bounded domains. Appl. Mech. Rev. 62, 020802 (2009)

    Article  Google Scholar 

  • S.B. Dalziel, Decay of rotating turbulence: Some particle tracking experiments. Appl. Sci. Res. 49(3), 217–244 (1992)

    Article  Google Scholar 

  • S.B. Dalziel, The twists and turns of rotating turbulence. J. Fluid Mech. 666, 1–4 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  • P.A. Davidson, Turbulence in Rotating. Stratified and Electrically Conducting Fluids (Cambridge University Press, 2013)

    Google Scholar 

  • P.A. Davidson, P.J. Staplehurst, S.B. Dalziel, On the evolution of eddies in a rapidly rotating system. J. Fluid Mech. 557, 135–144 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • L. Del Castello, Table-Top Rotating Turbulence: An Experimental Insight Through Particle Tracking. PhD Thesis, Eindhoven University of Technology, 2010

    Google Scholar 

  • L. Del Castello, H.J.H. Clercx, Lagrangian velocity autocorrelations in statistically steady rotating turbulence. Phys. Rev. E 83(5), 056316 (2011a)

    Google Scholar 

  • L. Del Castello, H.J.H. Clercx, Lagrangian acceleration of passive tracers in statistically steady rotating turbulence. Phys. Rev. Lett. 107(21), 214502 (2011b)

    Google Scholar 

  • L. Del Castello, H.J.H. Clercx, Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence. J. Turbul. 14(10), 19–36 (2013)

    Article  Google Scholar 

  • A. Delache, C. Cambon, F. Godeferd, Scale by scale anisotropy in freely decaying rotating turbulence. Phys. Fluids 26(2), 025104 (2014)

    Article  Google Scholar 

  • S.C. Dickinson, R.R. Long, Oscillating-grid turbulence including effects of rotation. J. Fluid Mech. 126, 315–333 (1983)

    Article  Google Scholar 

  • M.G. Dunn, Convective heat transfer and aerodynamics in axial flow turbines. J. Turbomach. 123(4), 637–686 (2001)

    Article  Google Scholar 

  • V.W. Ekman, On the influence of the Earth’s rotation on ocean currents. Arkiv för Matematik, Astronomi och Fysik 2(11), 1–52 (1905)

    MATH  Google Scholar 

  • U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, 1995)

    Google Scholar 

  • J. Gascard, A.J. Watson, M.J. Messias, K.A. Olsen, T. Johannesen, K. Simonsen, Long-lived vortices as a mode of deep ventilation in the Greenland Sea. Nature 416, 525–527 (2002)

    Article  Google Scholar 

  • F.S. Godeferd, L. Lollini, Direct Numerical simulations of turbulence with confinement and rotation. J. Fluid Mech. 393, 257–308 (1999)

    Article  MATH  Google Scholar 

  • F.S. Godeferd, F. Moisy, Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results. Appl. Mech. Rev. 67, 030802 (2015)

    Article  Google Scholar 

  • H.P. Greenspan, The Theory of Rotating Fluids (Cambridge University Press, 1968)

    Google Scholar 

  • S. Grossmann, D. Lohse, Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • D.L. Hartmann, L.A. Moy, Q. Fu, Tropical convection and the energy balance at the top of the atmosphere. J. Climate 14(24), 4495–4511 (2001)

    Article  Google Scholar 

  • E. Hopfinger, P. Browand, Y. Gagne, Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534 (1982)

    Article  Google Scholar 

  • A. Ibbetson, D.J. Tritton, Experiments on turbulence in a rotating fluid. J. Fluid Mech. 68, 639–672 (1975)

    Article  Google Scholar 

  • T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, A. Uno, Small-scale statistics in high-resolution direct numerical simulations of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335–366 (2007)

    Article  MATH  Google Scholar 

  • L. Jacquin, O. Leuchter, C. Cambon, J. Mathieu, Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1–52 (1990)

    Article  MATH  Google Scholar 

  • J.P. Johnston, Effects of system rotation on turbulence structure: a review to turbomachinery flows. Int. J. Rotat. Mach. 4(2), 97–112 (1998)

    Article  Google Scholar 

  • M. Kaczorowski, K.-L. Chong, K.-Q. Xia, Turbulent flow in the bulk of Rayleigh-Bénard convection: aspect-ratio dependence of the small-scale properties. J. Fluid Mech. 747, 73–102 (2014)

    Article  Google Scholar 

  • L.P. Kadanoff, Turbulent heat flow: structures and scaling. Phys. Today 54(8), 34–39 (2001)

    Article  Google Scholar 

  • Y. Kaneda, T. Ishihara, High-resolution direct numerical simulation of turbulence. J. Turbul. 7, N20 (2006)

    Article  Google Scholar 

  • R.H. Kraichnan, Inertial ranges in two-dimensional turbulence. Phys. Fluids 10(7), 1417–1423 (1967)

    Article  MathSciNet  Google Scholar 

  • R. Krishnamurti, L.N. Howard, Large-scale flow generation in turbulent convection. Proc. Natl. Acad. Sci. USA 78, 1981–1985 (1981)

    Article  Google Scholar 

  • P.K. Kundu, I.M. Cohen, D.R. Dowling, Fluid Mechanics (Academic Press, 2016)

    Google Scholar 

  • R.P.J. Kunnen, H.J.H. Clercx, B.J. Geurts, Breakdown of large-scale circulation in turbulent rotating convection. Europhys. Lett. 84(2), 24001 (2008a)

    Google Scholar 

  • R.P.J. Kunnen, H.J.H. Clercx, B.J. Geurts, Enhanced vertical inhomogeneity in turbulent rotating convection. Phys. Rev. Lett. 101(17), 174501 (2008b)

    Google Scholar 

  • R.P.J. Kunnen, B.J. Geurts, H.J.H. Clercx, Experimental and numerical investigation of turbulent convection in a rotating cylinder. J. Fluid Mech. 642, 445–476 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  • D. Lohse, K.-Q. Xia, Small-scale properties of turbulent Rayleigh-Bénard convection. Ann. Rev. Fluid Mech. 42, 335–364 (2010)

    Article  MATH  Google Scholar 

  • J.L. Lumley, G.R. Newman, The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161–178 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  • M.S. Miesch, The coupling of solar convection and rotation. Solar Phys. 192(1), 59–89 (2000)

    Article  Google Scholar 

  • P. Mininni, D. Rosenberg, A. Pouquet, Isotropisation at small scales of rotating helically driven turbulence. J. Fluid Mech. 699, 263–279 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  • F. Moisy, C. Morize, M. Rabaud, J. Sommeria, Decay laws, anisotropy and cyclone-anticyclone asymmetry in decaying rotating turbulence. J. Fluid Mech. 666, 5–35 (2011)

    Article  MATH  Google Scholar 

  • Y. Morinishi, K. Nakabayashi, S. Ren, A new DNS algorithm for rotating homogeneous decaying turbulence. Int. J. Heat Fluid Flow 22(1), 30–38 (2001)

    Article  Google Scholar 

  • C. Morize, F. Moisy, M. Rabaud, Decaying grid-generated turbulence in a rotating tank. Phys. Fluids 17(9), 095105 (2005)

    Article  MATH  Google Scholar 

  • W.-C. Müller, M. Thiele, Scaling and energy transfer in rotating turbulence. Europhys. Lett. 77(3), 34003 (2007)

    Article  Google Scholar 

  • R. Ni, S.D. Huang, K.-Q. Xia, Lagrangian acceleration measurements in convective thermal turbulence. J. Fluid Mech. 692, 395–419 (2012)

    Article  MATH  Google Scholar 

  • J. Pedlosky, Geophysical Fluid Dynamics (Springer, 1987)

    Google Scholar 

  • S.B. Pope, Turbulent Flows (Cambridge University Press, 2000)

    Google Scholar 

  • J. Proudman, On the motion of solids in a liquid possessing vorticity. Proc. R. Soc. A: Math. Phys. Eng. Sci. 92(642), 408–424 (1916)

    Article  MATH  Google Scholar 

  • H. Rajaei, P. Joshi, K.M.J. Alards, R.P.J. Kunnen, F. Toschi, H.J.H. Clercx, Transitions in turbulent rotating convection: a Lagrangian perspective. Phys. Rev. E 93(4), 043129 (2016)

    Article  Google Scholar 

  • H.T. Rossby, A study of Bénard convection with and without rotation. J. Fluid Mech. 36(2), 309–335 (1969)

    Article  Google Scholar 

  • J. Seiwert, C. Morize, F. Moisy, On the decrease of intermittency in decaying rotating turbulence. Phys. Fluids 20(7), 071702 (2008)

    Article  MATH  Google Scholar 

  • L.M. Smith, F. Waleffe, Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11(6), 1608–1622 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • P.J. Staplehurst, P.A. Davidson, S.B. Dalziel, Structure formation in homogeneous freely decaying rotating turbulence. J. Fluid Mech. 598, 81–106 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • R.J.A.M. Stevens, J.-Q. Zhong, H.J.H. Clercx, G. Ahlers, D. Lohse, Transitions between turbulent states in rotating Rayleigh-Bénard convection. Phys. Rev. Lett. 103(2), 024503 (2009)

    Article  Google Scholar 

  • R.J.A.M. Stevens, H.J.H. Clercx, D. Lohse, Heat transport and flow structure in rotating Rayleigh-Bénard convection. Eur. J. Fluid Mech. B/Fluids 40, 41–49 (2013)

    Article  Google Scholar 

  • G.I. Taylor, Motions of solids in fluids when the flow is not irrotational. Proce. R. Soc. A: Math. Phys. Eng. Sci. 93(648), 99–113 (1917)

    Article  MATH  Google Scholar 

  • T. Teitelbaum, P.D. Mininni, Large-scale effects on the decay of rotating helical and non-helical turbulence. Physica Scripta 2010, 014003 (2010)

    Article  Google Scholar 

  • T. Teitelbaum, P.D. Mininni, The decay of turbulence in rotating flows. Phys. Fluids 23(6), 065105 (2011)

    Article  Google Scholar 

  • M. Thiele, W.-C. Müller, Structure and decay of rotating homogeneous turbulence. J. Fluid Mech. 637, 425–442 (2009)

    Article  MATH  Google Scholar 

  • L.J.A. van Bokhoven, H.J.H. Clercx, G.J.F. van Heijst, R.R. Trieling, Experiments on rapidly rotating turbulent flows. Phys. Fluids 21(9), 096601 (2009)

    Article  MATH  Google Scholar 

  • H. van Santen, C.R. Kleijn, H.E.A. van den Akker, On turbulent flows in cold-wall CVD reactors. J. Crystal Growth 212(1–2), 299–310 (2000)

    Article  Google Scholar 

  • P. Wadhams, J. Holfort, E. Hansen, J.P. Wilkinson, A deep convective chimney in the winter Greenland Sea. Geophys. Res. Lett. 29(10), 1434–1437 (2002)

    Article  Google Scholar 

  • P.K. Yeung, Y. Zhou, Numerical study of rotating turbulence with external forcing. Phys. Fluids 10(11), 2895–2909 (1998)

    Article  Google Scholar 

  • M. Yokokawa, K. Itakura, A. Uno, T. Ishihara, Y. Kaneda, 16.4-Tflops direct numerical simulation of turbulence by a Fourier spectral method on the Earth simulator, in Proceedings IEEE/ACM SC2002 Conference, Baltimore, 2002, http://www.supercomputing.org/sc2002/paperpdfs/pap.pap273.pdf

  • K. Yoshimatsu, M. Midorikawa, Y. Kaneda, Columnar eddy formation in freely decaying homogeneous rotating turbulence. J. Fluid Mech. 677, 154–178 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  • J.-Q. Zhong, R.J.A.M. Stevens, H.J.H. Clercx, R. Verzicco, D. Lohse, G. Ahlers, Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Bénard convection. Phys. Rev. Lett. 102(4), 044502 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, 513, 5600MB, Eindhoven, The Netherlands

    Herman J. H. Clercx

  2. J.M. Burgers Center for Fluid Dynamics, Eindhoven, The Netherlands

    Herman J. H. Clercx

Authors
  1. Herman J. H. Clercx
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Herman J. H. Clercx .

Editor information

Editors and Affiliations

  1. Department of Applied Physics, University of Technology Eindhoven Department of Applied Physics, Eindhoven, The Netherlands

    Herman J.H. Clercx

  2. University of Technology Eindhoven , Eindhoven, Noord-Brabant, The Netherlands

    GertJan F. Van Heijst

Rights and permissions

Reprints and permissions

Copyright information

© 2018 CISM International Centre for Mechanical Sciences

About this chapter

Cite this chapter

Clercx, H.J.H. (2018). Transport Phenomena in Rotating Turbulence. In: Clercx, H., Van Heijst, G. (eds) Mixing and Dispersion in Flows Dominated by Rotation and Buoyancy. CISM International Centre for Mechanical Sciences, vol 580. Springer, Cham. https://doi.org/10.1007/978-3-319-66887-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66887-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66886-4

  • Online ISBN: 978-3-319-66887-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation