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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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Figures

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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.

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Fig. 1

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

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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).

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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.

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Fig. 6

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

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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).

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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.

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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).

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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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