Chinese Annals of Mathematics, Series B

, Volume 40, Issue 6, pp 869–890 | Cite as

Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

  • Di QiEmail author
  • Andrew J. MajdaEmail author


A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence. The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima (MHM for short) model, which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima (CHM for short) model for both plasma and geophysical flows. The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state. Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model, while stabilizing damping effect is shown with a zonal flow base state. Together with the selective decay effect from the dissipation, the secondary instability offers a complete characterization of the convergence process to the purely zonal structure. Direct numerical simulations with and without dissipation are carried out to confirm the instability theory. It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration. In comparison, the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.

Key words

Zonal flow generation Drift wave turbulence Secondary instability Modified Hasegawa-Mima model 

2000 MR Subject Classification

76F06 35Q60 76E25 


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Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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