Transient Metastability and Selective Decay for the Coherent Zonal Structures in Plasma Drift Wave Turbulence

  • Di QiEmail author
  • Andrew J. Majda


The emergence of persistent zonal structures is studied in freely decaying plasma flows. The plasma turbulence with drift waves can be described qualitatively by the modified Hasegawa–Mima (MHM) model, which is shown to create enhanced zonal jets and more physically relevant features compared with the original Charney–Hasegawa–Mima model. We analyze the generation and stability of the zonal state in the MHM model following the strategy of the selective decay principle. The selective decay and metastable states are defined as critical points of the enstrophy at constant energy. The critical points are first shown to be invariant solutions to the MHM equation with a special emphasis on the zonal modes, but the metastable states consist of a zonal state plus drift waves with a specific smaller wavenumber. Further, it is found with full mathematical rigor that any initial state will converge to some critical point solution at the long-time limit under proper dissipation forms, while the zonal states are the only stable ones. The selective decay process of the solutions can be characterized by the transient visits to several metastable states, then the final convergence to a purely zonal state. The selective decay and metastability properties are confirmed by numerical simulations with distinct initial structures. One highlight in both theory and numerics is the tendency of Landau damping to destabilize the selective decay process.


Zonal flows Selective decay principle Modified Hasegawa–Mima model 

Mathematics Subject Classification

35Q35 76F25 76X05 



A. J. M. is partially supported by the Office of Naval Research through MURI N00014-16-1-2161 and DARPA through W911NF-15-1-0636. D. Q. is supported as a postdoctoral fellow on both grants.


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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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