Acta Mechanica

, Volume 227, Issue 8, pp 2403–2413 | Cite as

Decay of isotropic flow and anisotropic flow with rotation or magnetic field or both in a weakly nonlinear regime

Original Paper

Abstract

We investigate numerically the decay of isotropic, rotating, magnetohydrodynamic (MHD) and rotating MHD flows in a periodic box. The Reynolds number Re defined by the box size and the initial velocity is 100, at which the flows are in a weakly nonlinear regime, i.e. not laminar but far away from the fully turbulent state. The decay of isotropic flow has two stages, the first stage for the development of small scales and the second stage for the viscous dissipation. In the rapidly rotating flow, fast rotation induces the inertial wave and causes the large-scale structure to inhibit the development of the first stage and retard the flow decay. In the MHD flow, the imposed field also causes the large-scale structure but facilitates the flow decay in the first stage because of the energy conversion from flow to magnetic field. The magnetic Reynolds number Rm is important for the dynamics of the MHD flow; namely, a high Rm induces the Alfvén wave but a low Rm can not. In the rotating MHD flow, slower rotation tends to convert more kinetic energy to magnetic energy. The orientation between the rotational and magnetic axes is important for the dynamics of the rotating MHD flow; namely, the energy conversion is more efficient and a stronger wave is induced when the two axes are not parallel than when they are parallel.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Davidson, P.A.: An Introduction to Magnetohydrodynamics. Cambridge University Press, Cambridge (2001)CrossRefMATHGoogle Scholar
  2. 2.
    Davidson, P.A.: Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, Oxford (2004)MATHGoogle Scholar
  3. 3.
    Davidson, P.A.: On the decay of Saffman turbulence subject to rotation, stratification or an imposed magnetic field. J. Fluid Mech. 663, 268–292 (2010)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Goldreich, P., Sridhar, S.: Magnetohydrodynamic turbulence revisited. Astrophys. J. 485, 680–688 (1997)CrossRefGoogle Scholar
  5. 5.
    Greenspan, H.P.: Theory of Rotating Fluids. Cambridge Univeresity Press, Cambridge (1968)MATHGoogle Scholar
  6. 6.
    Ishida, T., Davidson, P.A., Kaneda, Y.: On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Lee, E., Brachet, M.E., Pouquet, A., Mininni, P.D., Rosenberg, D.: Lack of universality in decaying magnetohydrodynamic turbulence. Phys. Rev. E 81, 016318 (2010)CrossRefGoogle Scholar
  8. 8.
    Moffatt, H.K.: On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571–592 (1967)CrossRefGoogle Scholar
  9. 9.
    Moffatt, H.K.: Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press, Cambridge (1978)Google Scholar
  10. 10.
    Okamoto, N., Davidson, P.A., Kaneda, Y.: On the decay of low-magnetic-Reynolds-number turbulence in an imposed magnetic field. J. Fluid Mech. 651, 295–318 (2010)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Reddy, K.S., Verma, M.K.: Strong anisotropy in quasi-static magnetohydrodynamic turbulence for high interaction parameters. Phys. Fluids 26, 025109 (2014)CrossRefGoogle Scholar
  12. 12.
    Sreenivasan, B., Alboussiére, T.: Experimental study of a vortex in a magnetic field. J. Fluid Mech. 464, 287–309 (2002)CrossRefMATHGoogle Scholar
  13. 13.
    Staplehurst, P.J., Davidson, P.A., Dalziel, S.B.: Structure formation in homogeneous freely decaying rotating turbulence. J. Fluid Mech. 598, 81–105 (2008)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Teitelbaum, T., Mininni, P.D.: The decay of turbulence in rotating flows. Phys. Fluids 23(6), 065105 (2011)CrossRefGoogle Scholar
  15. 15.
    Thiele, M., Müller, W.C.: Structure and decay of rotating homogeneous turbulence. J. Fluid Mech. 637, 425–442 (2009)CrossRefMATHGoogle Scholar
  16. 16.
    Wan, M., Oughtona, S., Servidioa, S., Matthaeus, W.H.: von Karman self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality. J. Fluid Mech. 697, 296–315 (2012)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Institute of Natural Sciences and Department of Physics and AstronomyShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Princeton University ObservatoryPrincetonUSA

Personalised recommendations