Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-09T22:19:30.916Z Has data issue: false hasContentIssue false
  • English
  • Français

Structure and decay of rotating homogeneous turbulence

Published online by Cambridge University Press:  21 September 2009

MARK THIELE  and
WOLF-CHRISTIAN MÜLLER
MARK THIELE
Affiliation:
Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
WOLF-CHRISTIAN MÜLLER*
Affiliation:
Max-Planck-Institut für Plasmaphysik, D-85748 Garching, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Navier–Stokes turbulence subject to solid-body rotation is studied by high-resolution direct numerical simulations (DNS) of freely decaying and stationary flows. Setups characterized by different Rossby numbers are considered. In agreement with experimental results strong rotation is found to lead to anisotropy of the direct nonlinear energy flux, which is attenuated primarily in the direction of the rotation axis. In decaying turbulence the evolution of kinetic energy follows an approximate power law with a distinct dependence of the decay exponent on the rotation frequency. A simple phenomenological relation between exponent and rotation rate reproduces this observation. Stationary turbulence driven by large-scale forcing exhibits k⊥−2-scaling in the rotation-dominated inertial range of the one-dimensional energy spectrum taken perpendicularly to the rotation axis. The self-similar scaling is shown to be the cumulative result of individual spectral contributions which, for low rotation rate, display k⊥−3-scaling near the k∥ = 0 plane. A phenomenology which incorporates the modification of the energy cascade by rotation is proposed. In the observed regime the nonlinear turbulent interactions are strongly influenced by rotation but not suppressed. Longitudinal two-point velocity structure functions taken perpendicularly to the axis of rotation indicate weak intermittency of the k∥ = 0 (2D) component of the flow while the intermittent scaling of k∥ ≠ 0 (3D) fluctuations is well captured by a modified She–Lévêque intermittency model which yields the expression ζp = p/6 + 2(1 − (2/3)p/2) for the structure function scaling exponents.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 637 , 25 October 2009 , pp. 425 - 442
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Babin, A., Mahalov, A. & Nicolaenko, B. 2000 Global regularity of 3D rotating Navier–Stokes equations for resonant domains. Appl. Math. Lett. 13, 51–57.CrossRefGoogle Scholar
Bardina, J., Ferziger, J. H. & Rogallo, R. S. 1985 Effect of rotation on isotropic turbulence: computation and modelling. J. Fluid Mech. 154, 321–336.CrossRefGoogle Scholar
Baroud, C. N., Plapp, B. B., She, Z.-S. & Swinney, H. L. 2002 Anomalous self-similarity in a turbulent rapidly rotating fluid. Phys. Rev. Lett. 88 (11), 114501.CrossRefGoogle Scholar
Baroud, C. N., Plapp, B. B., Swinney, H. L. & She, Z.-S. 2003 Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows. Phys. Fluids 15 (8), 2091–2104.CrossRefGoogle Scholar
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
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48 (1), R29–R32.CrossRefGoogle ScholarPubMed
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. & 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.CrossRefGoogle Scholar
Canuto, V. M. & Dubovikov, M. S. 1997 A dynamical model for turbulence. V. The effect of rotation. Phys. Fluids 9 (7), 2132–2140.CrossRefGoogle Scholar
Chen, Q., Chen, S., Eyink, G. & Holm, D. D. 2005 Resonant interactions in rotating homogeneous three-dimensional turbulence. J. Fluid Mech. 542, 139–164.CrossRefGoogle Scholar
Galtier, S. 2003 Weak intertial-wave turbulence theory. Phys. Rev. E 68, 015301.CrossRefGoogle ScholarPubMed
Godeferd, F. S. & Lollini, L. 1999 Direct numerical simulations of turbulence with confinement and rotation. J. Fluid Mech. 393, 257–307.CrossRefGoogle Scholar
Grauer, R., Krug, J. & Marliani, C. 1994 Scaling of high-order structure functions in magnetohydrodynamic turbulence. Phys. Lett. A 195, 335–338.CrossRefGoogle Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Hattori, Y., Rubinstein, R. & Ishizawa, A. 2004 Shell model for rotating turbulence. Phys. Rev. E 70, 046311.CrossRefGoogle ScholarPubMed
Hopfinger, E. J., Browand, F. K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534.CrossRefGoogle Scholar
Hossain, M. 1994 Reduction in the dimensionality of turbulence due to strong rotation. Phys. Fluids 6 (3), 1077–1080.CrossRefGoogle Scholar
Ibbetson, A. & Tritton, D. J. 1975 Experiments on turbulence in a rotating fluid. J. Fluid Mech. 68 (4), 639–672.CrossRefGoogle Scholar
Iroshnikov, P. S. 1964 Turbulence of a conducting fluid in a strong magnetic field. Sov. Astron. 7, 566–571 [Astron. Zh., 40:742, 1963].Google 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
Kolmogorov, A. N. 1941 On the degeneration of isotropic turbulence in an incompressible viscous liquid. Dokl. Akad. Nauk SSSR 31, 538–540.Google Scholar
Kraichnan, R. H. 1965 Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8 (7), 1385–1387.CrossRefGoogle Scholar
Lesieur, M. 1997 Turbulence in Fluids. Kluwer Academic Publishers.CrossRefGoogle Scholar
Mahalov, A. & Zhou, Y. 1996 Analytical and phenomenological studies of rotating turbulence. Phys. Fluids 8 (8), 2138–2152.CrossRefGoogle Scholar
Mansour, N. N., Cambon, C. & Speziale, C. G. 1992 Theoretical and computational study of rotating isotropic turbulence. In Studies in Turbulence (ed. Gatski, T. B., Sarkar, S. & Speziale, C. G.), pp. 59–75. Springer.CrossRefGoogle Scholar
Meneguzzi, M. & Pouquet, A. 1989 Turbulent dynamos driven by convection. J. Fluid Mech. 205, 297–318.CrossRefGoogle Scholar
Mininni, P. D., Alexakis, A. & Pouquet, A. 2009 Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers. Phys. Fluids 21, 015108.CrossRefGoogle Scholar
Mohamed, M. S. & LaRue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.CrossRefGoogle Scholar
Morinishi, Y., Nakabayashi, K. & Ren, S. Q. 2001 Dynamics of anisotropy on decaying homogeneous turbulence subjected to system rotation. Phys. Fluids 13 (10), 2912–2922.CrossRefGoogle Scholar
Morize, C. & Moisy, F. 2006 Energy decay of rotating turbulence with confinement effects. Phys. Fluids 18 (065107).CrossRefGoogle Scholar
Morize, C., Moisy, F. & Rabaud, M. 2005 Decaying grid-generated turbulence in a rotating tank. Phys. Fluids 17 (095105).CrossRefGoogle Scholar
Müller, W.-C. & Biskamp, D. 2000 Scaling properties of three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 84 (3), 475–478.CrossRefGoogle ScholarPubMed
Müller, W.-C. & Thiele, M. 2007 Scaling and energy transfer in rotating turbulence. Europhys. Lett. 77 (34003).CrossRefGoogle Scholar
Ozmidov, R. V. 1992 Length scales and dimensionless numbers in a stratified ocean. Oceanology 32 (3), 259–262.Google Scholar
Politano, H. & Pouquet, A. 1995 Model of intermittency in magnetohydrodynamic turbulence. Phys. Rev. E 52 (1), 636–641.CrossRefGoogle ScholarPubMed
Saffman, P. G. 1967 Note on decay of homogeneous turbulence. Phys. Fluids 10, 1349–1352.CrossRefGoogle Scholar
Seiwert, J., Morize, C. & Moisy, F. 2008 On the decrease of intermittency in decaying rotating turbulence. Phys. Fluids 20, 071702.CrossRefGoogle Scholar
She, Z.-S. & Lévêque, E. 1994 Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72 (3), 336–339.CrossRefGoogle ScholarPubMed
Smith, L. M. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11 (6), 1608–1622.CrossRefGoogle Scholar
Squires, K. D., Chasnov, J. R., Mansour, N. N. & Cambon, C. 1993 Investigation of the asymptotic state of rotating turbulence using large-eddy simulation. In Annual Research Briefs, pp. 157–170. Centre for Turbulence Research, Stanford University.Google Scholar
Wigeland, R. A. 1978 Grid generated turbulence with and without rotation about the streamwise direction. PhD thesis, Illinois Institute of Technology.Google Scholar
Yang, X. & Domaradzki, J. A. 2004 Large eddy simulation of decaying rotating turbulence. Phys. Fluids 16 (11), 4088–4104.CrossRefGoogle Scholar
Yeung, P. K. & Zhou, Y. 1998 Numerical study of rotating turbulence with external forcing. Phys. Fluids 10 (11), 2895–2909.CrossRefGoogle Scholar
Zeman, O. 1994 A note on the spectra and decay of rotating homogeneous turbulence. Phys. Fluids 6 (10), 3221–3223.CrossRefGoogle Scholar
Zhou, Y. 1995 A phenomenological treatment of rotating turbulence. Phys. Fluids 7 (8), 2092–2094.CrossRefGoogle Scholar