### Abstract

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.

Original language | English (US) |
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Journal | Journal of Nonlinear Science |

DOIs | |

State | Published - Jan 1 2019 |

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### Keywords

- Modified Hasegawa–Mima model
- Selective decay principle
- Zonal flows

### ASJC Scopus subject areas

- Modeling and Simulation
- Engineering(all)
- Applied Mathematics

### Cite this

**Transient Metastability and Selective Decay for the Coherent Zonal Structures in Plasma Drift Wave Turbulence.** / Qi, Di; Majda, Andrew.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Transient Metastability and Selective Decay for the Coherent Zonal Structures in Plasma Drift Wave Turbulence

AU - Qi, Di

AU - Majda, Andrew

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Modified Hasegawa–Mima model

KW - Selective decay principle

KW - Zonal flows

UR - http://www.scopus.com/inward/record.url?scp=85064434265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064434265&partnerID=8YFLogxK

U2 - 10.1007/s00332-019-09544-5

DO - 10.1007/s00332-019-09544-5

M3 - Article

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

ER -