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Review Article

Structure and Dynamics of Rotating Turbulence: A Review of Recent Experimental and Numerical Results

[+] Author and Article Information
Fabien S. Godeferd

LMFA UMR 5509 CNRS,
École centrale de Lyon,
Université de Lyon,
Écully 69134, France
e-mail: fabien.godeferd@ec-lyon.fr

Frédéric Moisy

FAST UMR 7608 CNRS,
Université Paris-Sud,
Orsay 91405, France
e-mail: frederic.moisy@fast.u-psud.fr

1Corresponding author.

Manuscript received January 10, 2014; final manuscript received October 30, 2014; published online January 15, 2015. Assoc. Editor: Herman J. H. Clercx.

Appl. Mech. Rev 67(3), 030802 (May 01, 2015) (13 pages) Paper No: AMR-14-1004; doi: 10.1115/1.4029006 History: Received January 10, 2014; Revised October 30, 2014; Online January 15, 2015

Rotating turbulence is a fundamental phenomenon appearing in several geophysical and industrial applications. Its study benefited from major advances in the recent years, but also raised new questions. We review recent results for rotating turbulence, from several numerical and experimental researches, and in relation with theory and models, mostly for homogeneous flows. We observe a convergence in the statistical description of rotating turbulence from the advent of modern experimental techniques and computational power that allows to investigate the structure and dynamics of rotating flows at similar parameters and with similar description levels. The improved picture about the anisotropization mechanisms, however, reveals subtle differences in the flow conditions, including its generation and boundary conditions, which lead to separate points of view about the role of linear mechanisms—the Coriolis force and inertial waves—compared with more complex nonlinear triadic interactions. This is discussed in relation with the most recent diagnostic of dynamical equations in physical and spectral space.

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References

Barnes, S. A., 2001, “An Assessment of the Rotation Rates of the Host Stars of Extrasolar Planets,” Astrophys. J., 561(2), pp. 1095–1106. [CrossRef]
Cho, J. Y.-K., Menou, K., Hansen, B. M. S., and Seager, S., 2008, “Atmospheric Circulation of Close-in Extrasolar Giant Planets: I. Global, Barotropic, Adiabatic Simulations,” Astrophys. J., 675(1), pp. 817–845. [CrossRef]
Dumitrescu, H., and Cardos, V., 2004. “Rotational Effects on the Boundary-Layer Flow in Wind Turbines,” AIAA J., 42(2), pp. 408–411. [CrossRef]
Praud, O., Sommeria, J., and Fincham, A., 2006, “Decaying Grid Turbulence in a Rotating Stratified Fluid,” J. Fluid Mech., 547, p. 389. [CrossRef]
Sagaut, P., and Cambon, C., 2008, Homogeneous Turbulence Dynamics, Cambridge University, Cambridge, UK [CrossRef].
Greenspan, H. P., 1968, The Theory of Rotating Fluids, Cambridge University, Cambridge, UK.
Bennetts, D. A., and Hocking, L. M., 1973, “On Nonlinear Ekman and Stewartson Layers in a Rotating Fluid,” Proc. R. Soc. London, Ser. A, 333(1595), pp. 469–489. [CrossRef]
Taylor, G. I., 1917, “Motion of Solids in Fluids When The Flow Is Not Irrotational,” Proc. R. Soc. London, Ser. A, 93(648), pp. 99–113. [CrossRef]
Proudman, J., 1916, “On the Motion of Solids in a Liquid Possessing Vorticity,” Proc. R. Soc. London, Ser. A, 92(642), pp. 408–424. [CrossRef]
Babin, A., Mahalov, A., and Nicolaenko, B., 2000, “Global Regularity of 3D Rotating Navier-Stokes Equations for Resonant Domains,” Appl. Math. Lett., 13(4), pp. 51–57. [CrossRef]
Zeman, O., 1994, “A Note on the Spectra and Decay of Rotating Homogeneous Turbulence,” Phys. Fluids, 6(10), p. 3221. [CrossRef]
Batchelor, G. K., 2000, An Introduction to Fluid Dynamics, Cambridge University, Cambridge, UK [CrossRef].
Mininni, P. D., and Pouquet, A., 2010, “Rotating Helical Turbulence. I. Global Evolution and Spectral Behavior,” Phys. Fluids, 22(3), p. 035105. [CrossRef]
Lamriben, C., Cortet, P.-P., and Moisy, F., 2011, “Direct Measurements of Anisotropic Energy Transfers in a Rotating Turbulence Experiment,” Phys. Rev. Lett., 107, p. 024503. [CrossRef] [PubMed]
Davidson, P. A., 2013, Turbulence in Rotating, Stratified and Electrically Conducting Fluids, Cambridge University, New York [CrossRef].
Lighthill, M., 1978, Waves in Fluids, Cambridge University, New York.
Görtler, H., 1957, “On Forced Oscillations in Rotating Fluids,” Proceedings of the Fifth Midwestern Conference on Fluid Mechanics, The University of Michigan, Ann Arbor, MI, Apr. 1–2, pp. 1–10.
Cortet, P.-P., Lamriben, C., and Moisy, F., 2010, “Viscous Spreading of an Inertial Wave Beam in a Rotating Fluid,” Phys. Fluids, 22(8), p. 086603. [CrossRef]
Maas, L. R. M., 2001, “Wave Focusing and Ensuing Mean Flow due to Symmetry Breaking in Rotating Fluids,” J. Fluid Mech., 437, pp. 13–28. [CrossRef]
Nazarenko, S., 2011, Wave Turbulence, Springer, Berlin [CrossRef].
Smith, L. M., and Lee, Y., 2005, “On Near Resonances and Symmetry Breaking in Forced Rotating Flows at Moderate Rossby Number,” J. Fluid Mech., 535, p. 111. [CrossRef]
Bourouiba, L., Straube, D. N., and Waite, M. L., 2012, “Non-Local Energy Transfers in Rotating Turbulence at Intermediate Rossby Number,” J. Fluid Mech., 690, pp. 129–147. [CrossRef]
Bourouiba, L., 2008, “Discreteness and Resolution Effects in Rapidly Rotating Turbulence,” Phys. Rev. E, 78, p. 056309. [CrossRef]
Smith, L., and Waleffe, F., 1999, “Transfer of Energy to Two-Dimensional Large Scales in Forced, Rotating Three-Dimensional Turbulence,” Phys. Fluids, 11(6), pp. 1608–1622. [CrossRef]
Bourouiba, L., and Bartello, P., 2007, “The Intermediate Rossby Number Range and Two-Dimensional–Three-Dimensional Transfers in Rotating Decaying Homogeneous Turbulence,” J. Fluid Mech., 587, pp. 139–161. [CrossRef]
Scott, J., 2014, “Wave Turbulence in a Rotating Channel,” J. Fluid Mech., 741, pp. 316–349. [CrossRef]
Wigeland, R. A., and Nagib, H. M., 1978, “Grid-Generated Turbulence With and Without Rotation About the Streamwise Direction,” IIT Fluid and Heat Transfer Report No. R78-1, Illinois Institute of Technology, Chicago, IL.
Jacquin, L., Leuchter, O., Cambon, C., and Mathieu, J., 1990, “Homogeneous Turbulence in the Presence of Rotation,” J. Fluid Mech., 220, pp. 1–52. [CrossRef]
Ibbetson, A., and Tritton, D. J., 1975, “Experiments on Turbulence in a Rotating Fluid,” J. Fluid Mech., 68(4), pp. 639–672. [CrossRef]
Dalziel, S., 1992, “Decay of Rotating Turbulence: Some Particle Tracking Experiments,” Appl. Sci. Res., 49(3), pp. 217–244. [CrossRef]
Morize, C., Moisy, F., and Rabaud, M., 2005, “Decaying Grid-Generated Turbulence in a Rotating Tank,” Phys. Fluids, 17(9), p. 095105. [CrossRef]
Staplehurst, P. J., Davidson, P. A., and Dalziel, S. B., 2008, “Structure Formation in Homogeneous, Freely Decaying, Rotating Turbulence,” J. Fluid Mech., 598, pp. 81–103. [CrossRef]
Moisy, F., Morize, C., Rabaud, M., and Sommeria, J., 2011, “Decay Laws, Anisotropy and Cyclone-Anticyclone Anisotropy in Decaying Rotating Turbulence,” J. Fluid Mech., 666, pp. 5–35. [CrossRef]
Davidson, P. A., Staplehurst, P. J., and Dalziel, S. B., 2006, “On the Evolution of Eddies in a Rapidly Rotating System,” J. Fluid Mech., 557, pp. 135–144. [CrossRef]
Hopfinger, E., Browand, P., and Gagne, Y., 1982, “Turbulence and Waves in a Rotating Tank,” J. Fluid Mech., 125, p. 505. [CrossRef]
Dickinson, S. C., and Long, R. R., 1983, “Oscillating-Grid Turbulence Including Effects of Rotation,” J. Fluid Mech., 126, pp. 315–333. [CrossRef]
Bokhoven, L. J. A. V., Clercx, H. J. H., Heijst, G. J. F. V., and Trieling, R. R., 2009, “Experiments on Rapidly Rotating Turbulent Flows,” Phys. Fluids, 21(9), p. 096601. [CrossRef]
Baroud, C. N., Plapp, B. B., She, Z.-S., and Swinney, H. L., 2002, “Anomalous Self-Similarity in a Turbulent Rapidly Rotating Fluid,” Phys. Rev. Lett., 88, p. 114501. [CrossRef] [PubMed]
Del Castello, L., and Clercx, H. J. H., 2011, “Lagrangian Velocity Autocorrelations in Statistically Steady Rotating Turbulence,” Phys. Rev. E, 83(5), p. 056316. [CrossRef]
Lamriben, C., Cortet, P.-P., and Moisy, F., 2011, “Direct Measurements of Anisotropic Energy Transfers in a Rotating Turbulence Experiment,” Phys. Rev. Lett., 107(2), p. 024503. [CrossRef] [PubMed]
Kinzel, M., Holzner, M., Lüthi, B., Tropea, C., Kinzelbach, W., and Oberlack, M., 2009, “Experiments on the Spreading of Shear-Free Turbulence Under the Influence of Confinement and Rotation,” Exp. Fluids, 47(4–5), pp. 801–809. [CrossRef]
Kinzel, M., Wolf, M., Holzner, M., Lüthi, B., Tropea, C., and Kinzelbach, W., 2010, “Simultaneous Two-Scale 3D-PTV Measurements in Turbulence Under the Influence of System Rotation,” Exp. Fluids, 51(1), pp. 75–82. [CrossRef]
Ruppert-Felsot, J., Praud, O., Sharon, E., and Swinney, H., 2005, “Extraction of Coherent Structures in a Rotating Turbulent Flow Experiment,” Phys. Rev. E, 72(1), p. 016311. [CrossRef]
Kolvin, I., Cohen, K., Vardi, Y., and Sharon, E., 2009, “Energy Transfer by Inertial Waves During the Buildup of Turbulence in a Rotating System,” Phys. Rev. Lett., 102(1), p. 014503. [CrossRef] [PubMed]
Yarom, E., Vardi, Y., and Sharon, E., 2013, “Experimental Quantification of Inverse Energy Cascade in Deep Rotating Turbulence,” Phys. Fluids, 25(8), p. 085105. [CrossRef]
Del Castello, L., and Clercx, H. J. H., 2011, “Lagrangian Acceleration of Passive Tracers in Statistically Steady Rotating Turbulence,” Phys. Rev. Lett., 107(21), p. 214502. [CrossRef] [PubMed]
Del Castello, L., and Clercx, H. J., 2013, “Geometrical Statistics of the Vorticity Vector and the Strain Rate Tensor in Rotating Turbulence,” J. Turbul., 14(10), pp. 19–36. [CrossRef]
Gallet, B., Campagne, A., Cortet, P.-P., and Moisy, F., 2014, “Scale-Dependent Cyclone-Anticyclone Asymmetry in a Forced Rotating Turbulence Experiment,” Phys. Fluids, 26(3), p. 035108. [CrossRef]
Simand, C., Chillà, F., and Pinton, J.-F., 2000, “Inhomogeneous Turbulence in the Vicinity of a Large-Scale Coherent Vortex,” Europhys. Lett. (EPL), 49(3), pp. 336–342. [CrossRef]
Lamriben, C., Cortet, P.-P., Moisy, F., and Maas, L. R. M., 2011, “Excitation of Inertial Modes in a Closed Grid Turbulence Experiment Under Rotation,” Phys. Fluids, 23(1), p. 015102. [CrossRef]
Ferrero, E., Mortarini, L., Manfrin, M., Longhetto, A., Genovese, R., and Forza, R., 2009, “Boundary-Layer Stress Instabilities in Neutral, Rotating Turbulent Flows,” Boundary Layer Meteorol., 130(3), pp. 347–363. [CrossRef]
Bewley, G. P., Lathrop, D. P., Maas, L. R. M., and Sreenivasan, K. R., 2007, “Inertial Waves in Rotating Grid Turbulence,” Phys. Fluids, 19(7), p. 071701. [CrossRef]
Ott, S., and Mann, J., 2000, “An Experimental Investigation of the Relative Diffusion of Particle Pairs in Three-Dimensional Turbulent Flow,” J. Fluid Mech., 422, pp. 207–223. [CrossRef]
Morinishi, Y., Nakabayashi, K., and Ren, S., 2001, “A New DNS Algorithm for Rotating Homogeneous Decaying Turbulence,” Int. J. Heat Fluid Flow, 22(1), pp. 30–38. [CrossRef]
Brandenburg, A., Svedin, A., and Vasil, G. M., 2009, “Turbulent Diffusion With Rotation or Magnetic Fields,” Mon. Not. R. Astron. Soc., 395(3), pp. 1599–1606. [CrossRef]
Mininni, P., Rosenberg, D., and Pouquet, A., 2012, “Isotropisation at Small Scales of Rotating Helically Driven Turbulence,” J. Fluid Mech., 699, pp. 263–279. [CrossRef]
Yeung, P. K., and Zhou, Y., 1998, “Numerical Study of Rotating Turbulence With External Forcing,” Phys. Fluids, 10(11), pp. 2895–2909. [CrossRef]
Morinishi, Y., Nakabayashi, K., and Ren, S. Q., 2001, “Dynamics of Anisotropy on Decaying Homogeneous Turbulence Subjected to System Rotation,” Phys. Fluids, 13(10), pp. 2912–2922. [CrossRef]
Thiele, M., and Müller, W.-C., 2009, “Structure and Decay of Rotating Homogeneous Turbulence,” J. Fluid Mech., 637, pp. 425–442. [CrossRef]
Teitelbaum, T., and Mininni, P., 2010, “Large-Scale Effects on the Decay of Rotating Helical and Non-Helical Turbulence,” Phys. Scr., 2010, p. 014003. [CrossRef]
Yoshimatsu, K., Midorikawa, M., and Kaneda, Y., 2011, “Columnar Eddy Formation in Freely Decaying Homogeneous Rotating Turbulence,” J. Fluid Mech., 677, pp. 154–178. [CrossRef]
Delache, A., Cambon, C., and Godeferd, F., 2014, “Scale by Scale Anisotropy in Freely Decaying Rotating Turbulence,” Phys. Fluids, 26(2), p. 025104 [CrossRef].
Deusebio, E., Boffetta, G., Lindborg, E., and Musacchio, S., 2014, “Dimensional Transition in Rotating Turbulence,” Phys. Rev. E, 90, p. 023005. [CrossRef]
Dalziel, S. B., 2011, “The Twists and Turns of Rotating Turbulence,” J. Fluid Mech., 666, pp. 1–4. [CrossRef]
Teitelbaum, T., and Mininni, P. D., 2011, “The Decay of Turbulence in Rotating Flows,” Phys. Fluids, 23(6), p. 065105. [CrossRef]
Cambon, C., Mansour, N. N., and Godeferd, F. S., 1997, “Energy Transfer in Rotating Turbulence,” J. Fluid Mech., 337, pp. 303–332. [CrossRef]
Canuto, V. M., and Dubovikov, M. S., 1997, “A Dynamical Model for Turbulence. v. the Effect of Rotation,” Phys. Fluids, 9(7), pp. 2132–2140. [CrossRef]
Kraichnan, R. H., 1975, “Statistical Dynamics of Two-Dimensional Flow,” J. Fluid Mech., 67(1), pp. 155–175. [CrossRef]
Bellet, F., Godeferd, F. S., Scott, J. F., and Cambon, C., 2006, “Wave Turbulence in Rapidly Rotating Flows,” J. Fluid Mech., 562, pp. 83–121. [CrossRef]
Kassinos, S. C., Reynolds, W. C., and Roger, M. M., 2001, “One-Point Turbulence Structure Tensors,” J. Fluids. Mech., 428, pp. 213–248. [CrossRef]
Craya, A., 1958, “Contribution à l'analyse de la turbulence associée à des vitesses moyennes,” Rev. Sci. et Tech. du Ministère de l'Air (France), 345.
Herring, J. R., 1974, “Approach of Axisymmetric Turbulence to Isotropy,” Phys. Fluids, 17(5), pp. 859–872. [CrossRef]
Waleffe, F., 1993, “Inertial Transfers in the Helical Decomposition,” Phys. Fluids A, 5(3), p. 026310. [CrossRef]
Bartello, P., Metais, O., and Lesieur, M., 1994, “Coherent Structures in Rotating 3-Dimensional Turbulence,” J. Fluid Mech., 273, pp. 1–29. [CrossRef]
van Bokhoven, L., Cambon, C., Liechtenstein, L., Godeferd, F., and Clercx, H., 2008, “Refined Vorticity Statistics of Decaying Rotating Three-Dimensional Turbulence,” J. Turbul., 9, N6.
Gence, J. N., and Frick, C., 2001, “Birth of the Triple Correlations of Vorticity in an Homogeneous Turbulence Submitted to a Solid Body Rotation,” C. R. Acad. Sci. Paris, Série IIB, 329(4), pp. 351–356.
Sreenivasan, B., and Davidson, P. A., 2008, “On the Formation of Cyclones and Anticyclones in a Rotating Fluid,” Phys. Fluids, 20(8), p. 085104. [CrossRef]
Zhou, Y., 1995, “A Phenomenological Treatment of Rotating Turbulence,” Phys. Fluids, 7(8), pp. 2092–2094. [CrossRef]
Mahalov, A., and Zhou, Y., 1996, “Analytical and Phenomenological Studies of Rotating Turbulence,” Phys. Fluids, 8(8), pp. 2138–2152. [CrossRef]
Galtier, S., 2003, “Weak Inertial-Wave Turbulence Theory,” Phys. Rev. E, 68, p. 015301. [CrossRef]
Cambon, C., Rubinstein, R., and Godeferd, F. S., 2004, “Advances in Wave-Turbulence: Rapidly Rotating Flows,” New J. Phys., 6, 73. [CrossRef]
Galtier, S., 2014, “Theory for Helical Turbulence Under Fast Rotation,” Phys. Rev. E, 89, p. 041001. [CrossRef]
Frisch, U., 1995, Turbulence. The Legacy of A. N. Kolmogorov, Cambridge University, Cambridge [CrossRef].
Galtier, S., 2009, “Exact Vectorial Law for Homogeneous Rotating Turbulence,” Phys. Rev. E, 80(4), p. 046301. [CrossRef]
Godeferd, F., and Cambon, C., 1994, “Detailed Investigation of Energy Transfers in Homogeneous Stratified Turbulence,” Phys. Fluids, 6(6), pp. 2084–2100. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic of the different regimes of rotating turbulence in the Rossby–Reynolds parametric plane

Grahic Jump Location
Fig. 2

Propagation of inertial waves (a) viewed in the experiment by Görtler [17]. (Reproduced with permission from Greenspan [6]. Copyright 1968 by Cambridge University.) (b) Schematic indicating the conical-shaped isophase surfaces emanating from a point source, along which velocity propagates at the group velocity cg.

Grahic Jump Location
Fig. 4

Organization of turbulence in columnar structures: (a) visualization by pearlescence technique in an experiment by Staplehurst (see Table 1), as reported by Dalziel (false colors are applied to enhance the features of the flow). Turbulence decays behind a stroke of vertically towed grid, from left to right after 0.5, 1, 2, 4 inertial times Ω/2π after the grid left bottom of view. (Reproduced with permission from Dalziel [64]. Copyright 2011 by Cambridge University). (b) Isosurface of intense vorticity regions in a subregion of a 2563 Direct Numerical Simulation by Yoshimatsu et al., from left to right at initial time then at Ωt = 5 at which Roω ≃ 1, and at Ωt = 10 and 20. (Reproduced with permission from Yoshimatsu [61]. Copyright 2011 by Cambridge University).

Grahic Jump Location
Fig. 5

Evolution of the contributions b33e and b33z to the Reynolds stress anisotropic component b33 from (a) freely decaying simulations by Morinishi et al. (Reproduced with permission from Morinishi et al. [58]. Copyright 2001 by American Physical Society. (b) Simulations and EDQNM (Eddy Damped Quasi-Normal Markovian) model (dashed lines) presented in Cambon et al. (Reproduced with permission from Cambon et al. [66]. Copyright 1997 by Cambridge University). Time evolves from right to left as Rossby numbers decrease during the evolution.

Grahic Jump Location
Fig. 6

PDF of axial vorticity by Morize et al. (Reproduced with permission from Morize et al. [31]. Copyright 2005 by American Physical Society).

Grahic Jump Location
Fig. 7

Growth of axial vorticity skewness ⟨ωz3⟩/⟨ωz2⟩3/2 in experiments (top figures) and numerical simulations (bottom figures): (a) Experimental data by Staplehurst et al. filled and open symbols, respectively, at initial Ro ≃ 0.37 and 0.41, two different rotation rates used. (Reproduced with permission from Staplehurst et al. [32]. Copyright 2008 by Cambridge University.) (b) Experimental data by Morize et al. at Rog from 2.4 to 120. (Reproduced with permission from Morize et al. [31]. Copyright 2005 by American Physical Society). (c) DNS (direct numerical simulation) data by Yoshimatsu et al. with Ro from 4.8 × 10−2 to 0.24. (Reproduced with permission from Yoshimatsu et al. [61]. Copyright 2011 by Cambridge University). (d) DNS data by van Bokhoven et al. at Roλ from 0.073 to 0.37. (Reproduced with permission from van Bokhoven et al. [75]. Copyright 2008 by Taylor & Francis).

Grahic Jump Location
Fig. 8

Directional spectra E(k,θ) from (a) direction numerical simulations by Yoshimatsu et al. (Reproduced with permission from Yoshimatsu et al. [61]. Copyright 2011 by Cambridge University). (b) From the two-point statistical AQNM (asymptotic quasi-normal Markovian) model by Bellet et al. (Reproduced with permission from Bellet et al. [69]. Copyright 2006 by Cambridge University). The lower spectra are for the vertical direction θ ≃ π/2, the upper ones for the horizontal spectra at θ ≃ 0. In the simulations, four angular sectors of θ are used to compute the statistical averages, whereas in the AQNM model, spectra correspond to discrete orientations.

Grahic Jump Location
Fig. 9

Nonlinear transfer -∇·F measured experimentally by Lamriben et al. (top right sector), along with the flux itself F represented as a vector field in the bottom left sector, and its angle with respect to the radial direction in the bottom right sector. Dashed lines represent crests of maxima of |F| and of -∇·F in the top left and top right quadrants, respectively. (Reproduced with permission from Lamriben et al. [40]. Copyright 2011 by American Physical Society).

Grahic Jump Location
Fig. 10

Sketch of the structuration of rotating turbulence under the effects of (a) propagation of inertial waves from initial inhomogeneous turbulent structures as proposed by Staplehurst et al. (Reproduced with permission from Staplehurst et al. [32]. Copyright 2008 by Cambridge University). (b) Accumulation of energy in the vicinity of the two-dimensional manifold hence producing vertical vortices (as proposed, e.g., in Ref. [85]).

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