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Columnar eddy formation in freely decaying homogeneous rotating turbulence

Published online by Cambridge University Press:  18 April 2011

K. YOSHIMATSU ,
M. MIDORIKAWA  and
Y. KANEDA
K. YOSHIMATSU*
Affiliation:
Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan
M. MIDORIKAWA
Affiliation:
Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan
Y. KANEDA
Affiliation:
Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan
*
†Email address for correspondence: yosimatu@fluid.cse.nagoya-u.ac.jp
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Abstract

The roles of the Coriolis force and the convection associated with the fluid motion in the formation of columnar eddies in freely decaying homogeneous rotating turbulence at a moderate Rossby number are studied by direct numerical simulation of the Navier–Stokes equations in a periodic box. The simulated field is compared with a series of artificial fields generated by switching off the nonlinear and viscous terms in the Navier–Stokes equation at given instants. The comparison shows that, without the nonlinear convection effect, the Coriolis force cannot sustain the substantial growth in the direction parallel to the rotational axis of the length scale defined on the basis of the two-point correlation of the square of the vorticity, i.e. cannot sustain the formation of the columnar eddies. The length scale characterizes well the intuitive impression from visualization of flow obeying the dynamics with or without the nonlinear effect. It is shown that the lack of substantial growth is insensitive to the scale of the eddies, the box size and viscosity, at least in the case studied here.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Rotating turbulence

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 154 - 178
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Bartello, P., Métais, O. & Lesieur, M. 1994 Coherent structures in rotating three-dimensional turbulence. J. Fluid Mech. 273, 1–29.CrossRefGoogle Scholar
Bellet, F., Godeferd, F. S., Scott, J. F. & Cambon, C. 2006 Wave turbulence in rapidly rotating flows. J. Fluid Mech. 562, 83–121.CrossRefGoogle Scholar
van Bokhoven, L. J. A., Cambon, C., Liechtenstein, L., Godeferd, F. S. & Clercx, H. J. H. 2008 Refined vorticity statistics of decaying rotating three-dimensional turbulence. J. Turbul. 9 (6), 1–24.CrossRefGoogle Scholar
Bourouiba, L. & Bartello, P. 2007 The intermediate Rossby number range and two-dimensional–three-dimensional transfers in rotating decaying homogeneous turbulence. J. Fluid Mech. 587, 139–161.CrossRefGoogle Scholar
Cambon, C., Benoit, J. P., Shao, L. & Jacquin, L. 1994 Stability analysis and large-eddy simulation of rotating turbulence with organized eddies. J. Fluid Mech. 278, 175–200.Google Scholar
Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.CrossRefGoogle Scholar
Cambon, C., Mansour, N. N. & Godeferd, F. S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303–332.CrossRefGoogle Scholar
Cambon, C., Rubinstein, R. & Godeferd, F. S. 2004 Advances in wave turbulence: rapidly rotating flows. New J. Phys. 6, 73.Google Scholar
Cambon, C. & Scott, J. F. 1999 Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech. 31, 1–53.CrossRefGoogle Scholar
Chen, Q., Chen, S., Eyink, G. L. & Holm, D. D. 2005 Resonant interactions in rotating homogeneous three-dimensional turbulence. J. Fluid Mech. 542, 139–164.CrossRefGoogle Scholar
Craya, A. 1958 Contribution à l'analyse de la turbulence associée à des vitesses moyennes. P. S. T. Ministère de l'Air, p. 345.Google Scholar
Davidson, P. A., Staplehurst, P. J. & Dalziel, S. B. 2006 On the evolution of eddies in a rapidly rotating system. J. Fluid Mech. 557, 135–144.CrossRefGoogle Scholar
Galtier, S. 2003 Weak inertial-wave turbulence theory. Phys. Rev. E 68, 015301(R).CrossRefGoogle ScholarPubMed
Gence, J.-N. & Frick, C. 2001 Naissance des corrélations triples de vorticité dans une turbulence statistiquement homogène soumise à une rotation. C. R. Acad. Sci. Paris II B 329, 351–356.Google Scholar
Herring, J. R. 1974 Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859–872.Google Scholar
Hopfinger, E. J., Browand, F. K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534.Google Scholar
Hossain, M. 1994 Reduction in the dimensionality of turbulence due to a strong rotation. Phys. Fluids 6, 1077–1080.CrossRefGoogle Scholar
Jacquin, L., Leuchter, O., Cambon, C. & Mathieu, J. 1990 Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1–52.CrossRefGoogle Scholar
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.CrossRefGoogle Scholar
Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K. & Uno, A. 2003 Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15, L21–L24.CrossRefGoogle Scholar
Kolvin, I., Cohen, K., Vardi, Y., & Sharon, E. 2009 Energy transfer by inertial waves during the buildup of turbulence in a rotating system. Phys. Rev. Lett. 102, 014503.Google Scholar
Liechtenstein, L., Godeferd, F. S. & Cambon, C. 2005 Nonlinear formation of structures in rotating stratified turbulence. J. Turbul. 6 (24), 1–18.CrossRefGoogle Scholar
Moisy, F., Morize, C., Rabaud, M. & Sommeria, J. 2011 Decay laws, anisotropy and cyclone-anticyclone asymmetry in decaying rotating turbulence. J. Fluid Mech. 666, 5–35.CrossRefGoogle Scholar
Morinishi, Y., Nakabayashi, K. & Ren, S. Q. 2001 Dynamics of anisotropy on decaying homogeneous turbulence subjected to system rotation. Phys. Fluids 13, 2912–2922.Google Scholar
Morize, C., Moisy, F. & Rabaud, M. 2005 Decaying grid-generated turbulence in a rotating tank. Phys. Fluids 17, 095105.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Smith, L. M. & Lee, Y. 2005 On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number. J. Fluid Mech. 535, 111–142.Google Scholar
Smith, L. M. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11, 1608–1622.CrossRefGoogle Scholar
Squires, K. D., Chasnov, J. R., Mansour, N. N., & Cambon, C. 1994 The asymptotic state of rotating homogeneous turbulence at high Reynolds numbers. In Application of Direct and Large Eddy Simulation to Transition and Turbulence, Chania, Crete Greece.Google Scholar
Staplehurst, P. J., Davidson, P. A. & Dalziel, S. B. 2008 Structure formation in homogeneous freely decaying rotating turbulence. J. Fluid Mech. 598, 81–105.CrossRefGoogle Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids A 4, 350–363.CrossRefGoogle Scholar
Waleffe, F. 1993 Inertial transfers in the helical decomposition. Phys. Fluids A 5, 677–685.Google Scholar
Yeung, P. K. & Zhou, Y. 1998 Numerical study of rotating turbulence with external forcing. Phys. Fluids 10, 2895–2909.Google Scholar