Advertisement

Energy Fluxes and Shell-to-Shell Transfers in MHD Turbulence

  • Daniele Carati
  • Olivier Debliquy
  • Bernard Knaepen
  • Bogdan Teaca
  • Mahendra Verma
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 56)

Abstract

A spectral analysis of the energy cascade in magnetohydrodynamics (MHD) is presented using high resolution direct numerical simulations of both forced and decaying isotropic turbulence. The triad interactions between velocity and magnetic field modes are averaged into shell interactions between similar length scales phenomena. This is achieved by combining all the velocity Fourier modes that correspond to wave vectors with similar amplitude into a shell velocity variable. The same procedure is adopted for the magnetic field. The analysis of the interactions between these shell variables gives a global picture of the energy transfers between different length scales, as well as between the velocity and the magnetic fields. Also, two different attempts to separate the shell-to-shell interactions into forward and backward energy transfers are proposed. They provide diagnostics that can be used in order to assess subgrid-scale modelling in large-eddy simulation for turbulent MHD systems.

Keywords

Energy Transfer Triad Interaction Decay Turbulence Magnetic Prandtl Number Forced Turbulence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Kraichnan. Inertial-range transfer in two and three-dimensional turbulence, J. Fluid Mech. 47, pp. 525–535, 1971.zbMATHCrossRefGoogle Scholar
  2. [2]
    Y. Zhou. Degrees of locality of energy transfer in the inertial range, Phys. Fluids A 5, pp 1092–1094, 1993.CrossRefGoogle Scholar
  3. [3]
    R.M. Kerr, J.A. Domaradzki, and G. Barbier. Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence, Phys. Fluids 8, pp. 197–208, 1996.zbMATHCrossRefGoogle Scholar
  4. [4]
    A. Pouquet, U. Frisch, and J. Léorat. Strong MHD helical turbulence and the nonlinear dynamo effect, J. Fluid Mech. 77, pp. 321–354, 1976.zbMATHCrossRefGoogle Scholar
  5. [5]
    O. Schilling and Y. Zhou. Triadic energy transfers in non-helical magnetohydrodynamic turbulence, J. Plasma Phys. 68, pp 389–406, 2002.CrossRefGoogle Scholar
  6. [6]
    M.K. Verma. Statistical theory of magnetohydrodynamic turbulence: recent results, Phys. Report 401, pp 229–380, 2004.CrossRefGoogle Scholar
  7. [7]
    C.E. Leith. Stochastic backscatter in a subgrid-scale model: Plane shear mixing layer, Phys. Fluids A 2, pp 297–299, 1990.CrossRefGoogle Scholar
  8. [8]
    P.J. Mason and D.J. Thomson. Stochastic backscatter in large-eddy simulations of boundary layers, J. Fluid Mech. 242, pp 51–78, 1992.zbMATHCrossRefGoogle Scholar
  9. [9]
    D. Carati, S. Ghosal, and P. Moin. On the representation of backscatter in dynamic localization models, Phys. Fluids 7, pp 606–616, 1995.zbMATHCrossRefGoogle Scholar
  10. [10]
    O. Debliquy, M.K. Verma, and D. Carati. Energy fluxes and shell-toshell transfers in three-dimensional decaying magnetohydrodynamic turbulence, Phys. Plasmas 12, 042309, 2005.CrossRefGoogle Scholar
  11. [11]
    J.A. Domaradzki and R.S. Rogallo. Local energy-transfer and nonlocal interactions in homogeneous, isotropic turbulence, Phys. Fluids A 2, pp 413–426, 1990.CrossRefGoogle Scholar
  12. [12]
    G. Dar, M. Verma, and V. Eswaran. Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results, Physica D 3, pp 207–225, 2001.CrossRefGoogle Scholar
  13. [13]
    A. Alexakis, P.D. Mininni, and A. Pouquet. Shell to shell energy transfer in MHD, Part I: Steady state turbulence, Phys. Rev. E 72, p046301, 2005.CrossRefGoogle Scholar
  14. [14]
    P.D. Mininni, A. Alexakis, and A. Pouquet. Shell to shell energy transfer in MHD, Part II: Kinematic dynamo, Phys. Rev. E 72, p046302, 2005.CrossRefGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Daniele Carati
    • 1
  • Olivier Debliquy
    • 1
  • Bernard Knaepen
    • 1
  • Bogdan Teaca
    • 2
  • Mahendra Verma
    • 3
  1. 1.Statistical and Plasma PhysicsUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Faculty of PhysicsCraiovaRomania
  3. 3.Department of PhysicsI. I. T. KanpurKanpurIndia

Personalised recommendations