[Table of Contents]

Plasma and Fusion Research

Volume 1, 024 (2006)


Effect of Mean Flow on the Interaction between Turbulence and Zonal Flow
Ken UZAWA1), Yasuaki KISHIMOTO1,2) and Jiquan LI3)
Graduate School of Energy Science, Kyoto University
Naka Fusion Research Establishment
Southwestern Institute of Physics
(Received 26 January 2006 / Accepted 23 March 2006 / Published 17 May 2006)


The effects of an external mean flow on the generation of zonal flow in drift wave turbulence are theoretically studied in terms of a modulational instability analysis. A dispersion relation for the zonal flow instability having complex frequency ωq = Ωq + iγq is derived, which depends on the external mean flow's amplitude |φf| and radial wave number kf. As an example, we chose an ion temperature gradient (ITG) turbulence-driven zonal flow as the mean flow acting on an electron temperature gradient (ETG) turbulence-zonal flow system. The growth rate of the zonal flow γq is found to be suppressed, showing a relation γq = γq0(1-α|φf|2kf2 ), where γq0 is the growth rate in the absence of mean flow and α is a positive numerical constant. This formula is applicable to a strong shearing regime where the zonal flow instability is stabilized at α|φf2|kf2 ≈ 1. Meanwhile, the suppression is accompanied by an increase of the real frequency |Ωq|. The underlying physical mechanism of the suppression is discussed.


drift wave turbulence, zonal flow, mean plasma flow, modulational instability

DOI: 10.1585/pfr.1.024


  • [1] P.H. Diamond, S.-I. Itoh, K. Itoh and T.S. Hahm, Plasma Phys. Control. Fusion 47, R35 (2005).
  • [2] A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 59, 1581 (1987).
  • [3] L. Chen, Z. Lin and R. White, Phys. Plasmas 7, 3129 (2000).
  • [4] J.Q. Li and Y. Kishimoto, Phys. Plasmas 12, 054505 (2005).
  • [5] N. Miyato, Y. Kishimoto and J.Q. Li, Phys. Plasmas 11, 5557 (2004).
  • [6] T.S. Hahm and K.H. Burrell, Phys. Plasmas 3, 427 (1996).
  • [7] Y. Kishimoto, J.Y. Kim, W. Horton, T. Tajima, M.J. LeBrun and H. Shirai, Plasma Phys. Control. Fusion 41, A663 (1999).
  • [8] E. Kim and P. Diamond, Phys. Plasmas 10, 1698 (2003).
  • [9] A. Hasegawa and K. Mima, Phys. Fluids 21, 87 (1978).
  • [10] T.S. Hahm, M.A. Beer, Z. Lin, G.W. Hammett, W.W. Lee and W.M. Tang, Phys. Plasmas 6, 922 (1999).

This paper may be cited as follows:

Ken UZAWA, Yasuaki KISHIMOTO and Jiquan LI, Plasma Fusion Res. 1, 024 (2006).