Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T14:16:02.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian statistics of Navier–Stokes and MHD turbulence

Published online by Cambridge University Press:  01 December 2007

H. HOMANN ,
R. GRAUER ,
A. BUSSE  and
W. C. MÜLLER
H. HOMANN
Affiliation:
Theoretische Physik I, Ruhr-Universität Bochum, Germany ([email protected])
R. GRAUER
Affiliation:
Theoretische Physik I, Ruhr-Universität Bochum, Germany ([email protected])
A. BUSSE
Affiliation:
Theoretische Physik I, Ruhr-Universität Bochum, Germany ([email protected])
W. C. MÜLLER
Affiliation:
MPI for Plasma Physics, Garching, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to 10243 collocation points and 10 million particles in the Navier–Stokes case and 5123 collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al. (2004 New J. Phys.6, 116) and Xu et al. (2006 Phys. Rev. Lett.96, 024503). They differ from the simulations of Biferale et al. (2004 Phys. Rev. Lett.93, 064502) due to differences of the ranges chosen for evaluating the structure functions. In Navier–Stokes turbulence intermittency is stronger than predicted by the multifractal approach of Biferale et al. (2004 Phys. Rev. Lett.93, 064502) whereas in MHD turbulence the predictions from the multifractal approach are more intermittent than observed in our simulations. In addition, our simulations reveal that Lagrangian Navier–Stokes turbulence is more intermittent than MHD turbulence, whereas the situation is reversed in the Eulerian case. Those findings can not consistently be described by the multifractal modeling. The crucial point is that the geometry of the dissipative structures have different implications for Lagrangian and Eulerian intermittency. Application of the multifractal approach for the modeling of the acceleration probability density functions works well for the Navier–Stokes case but in the MHD case just the tails are well described.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 6 , December 2007 , pp. 821 - 830
Copyright
Copyright © Cambridge University Press 2007

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

[1]Ott, S. and Mann, J. 2000 J. Fluid Mech. 422, 207.CrossRefGoogle Scholar
[2]La Porta, A., Voth, G., Moisy, F. and Bodenschatz, E. 2000 Phys. Fluids 12, 1485.CrossRefGoogle Scholar
[3]La Porta, A., Voth, G., Crawford, A. M., Alexander, J. and Bodenschatz, E. 2001 Nature 409, 1017.Google Scholar
[4]Voth, G., La Porta, A., Crawford, A. M., Alexander, J. and Bodenschatz, E. 2001 Rev. Sci. Instrum. 12, 4348.CrossRefGoogle Scholar
[5]Mordant, N., Metz, P., Michel, O. and Pinton, J.-F. 2001 Phys. Rev. Lett. 87, 214501.Google Scholar
[6]Mordant, N., Lévêque, E. and Pinton, J.-F. 2004 New J. Phys. 6, 116.Google Scholar
[7]Friedrich, R. 2003 Phys. Rev. Lett. 90, 084501.CrossRefGoogle Scholar
[8]Biferale, L., Bofetta, G., Celani, A., Devinish, B. J., Lanotte, A. and Toschi, F. 2004 Phys. Rev. Lett. 93, 064502.CrossRefGoogle Scholar
[9]Xu, H., Bourgoin, M., Ouellette, N. and Bodenschatz, E. 2006 Phys. Rev. Lett. 96, 024503.Google Scholar
[10]Müller, W. C. and Biskamp, D. 2000 Phys. Rev. Lett. 84, 475.CrossRefGoogle Scholar
[11]Yeung, P. K. 2002 Annu. Rev. Fluid Mech. 34, 115.CrossRefGoogle Scholar
[12]Frisch, U. 1995 Turbulence. The Legacy of A. N. Kolmogorov. Cambridge: Cambridge University Press.Google Scholar
[13]Yeung, P. K. and Pope, S. B. 1989 J. Fluid Mech. 207, 531.Google Scholar
[14]Lässig, M. 2000 Phys. Rev. Lett. 84, 2618.Google Scholar
[15]Yakhot, V. and Sreenivasan, K. R. 2005 J. Stat. Phys. 121, 825.CrossRefGoogle Scholar
[16]Schumacher, J., Sreenivasan, K. R. and Yakhot, V. 2007 New J. Phys. 9, 89.CrossRefGoogle Scholar
[17]She, Z.-S. and Lévêque, E. 1994 Phys. Rev. Lett. 72, 336.CrossRefGoogle Scholar
[18]Dubrulle, B. 1994 Phys. Rev. Lett. 73, 959.Google Scholar
[19]Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. and Succi, S. 1993 Phys. Rev. E 48, R29.Google Scholar
[20]Yeung, P. K. and Borgas, M. S. 2004 J. Fluid Mech. 503, 93.CrossRefGoogle Scholar
[21]Biferale, L., Boffetta, G., Celani, A., Lanotte, A. and Toschi, F. 2005 Phys. Fluids 17, 021701.CrossRefGoogle Scholar
[22]Horbury, T. S. and Balogh, A. 1997 Nonlinear Proc. Geophys. 4, 185.CrossRefGoogle Scholar
[23]Li, Y. and Meneveau, C. 2005 Phys. Rev. Lett. 95, 164502.Google Scholar