skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Solitary zonal structures in subcritical drift waves: a minimum model

Abstract

Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows. However, the nature of these structures has not been fully understood yet. Here, we show that similar structures can be obtained within a reduced model, which complements the modified Hasegawa–Mima equation with a generic primary instability and a background shear flow. We also find that these structures can be qualitatively reproduced in the modified Hasegawa–Wakatani equation, which subsumes the reduced model as a limit. In particular, we illustrate that in both cases, the solitary zonal structures approximately satisfy the same 'equation of state', which is a local relation connecting the DW envelope with the zonal-flow velocity. Due to this generality, our reduced model can be considered as a minimum model for solitary zonal structures in subcritical DWs.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1606350
Grant/Contract Number:  
AC02-09CH11466
Resource Type:
Accepted Manuscript
Journal Name:
Plasma Physics and Controlled Fusion
Additional Journal Information:
Journal Volume: 62; Journal Issue: 4; Journal ID: ISSN 0741-3335
Publisher:
IOP Science
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Zhou, Yao, Zhu, Hongxuan, and Dodin, I. Y. Solitary zonal structures in subcritical drift waves: a minimum model. United States: N. p., 2020. Web. doi:10.1088/1361-6587/ab78f3.
Zhou, Yao, Zhu, Hongxuan, & Dodin, I. Y. Solitary zonal structures in subcritical drift waves: a minimum model. United States. doi:https://doi.org/10.1088/1361-6587/ab78f3
Zhou, Yao, Zhu, Hongxuan, and Dodin, I. Y. Tue . "Solitary zonal structures in subcritical drift waves: a minimum model". United States. doi:https://doi.org/10.1088/1361-6587/ab78f3. https://www.osti.gov/servlets/purl/1606350.
@article{osti_1606350,
title = {Solitary zonal structures in subcritical drift waves: a minimum model},
author = {Zhou, Yao and Zhu, Hongxuan and Dodin, I. Y.},
abstractNote = {Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows. However, the nature of these structures has not been fully understood yet. Here, we show that similar structures can be obtained within a reduced model, which complements the modified Hasegawa–Mima equation with a generic primary instability and a background shear flow. We also find that these structures can be qualitatively reproduced in the modified Hasegawa–Wakatani equation, which subsumes the reduced model as a limit. In particular, we illustrate that in both cases, the solitary zonal structures approximately satisfy the same 'equation of state', which is a local relation connecting the DW envelope with the zonal-flow velocity. Due to this generality, our reduced model can be considered as a minimum model for solitary zonal structures in subcritical DWs.},
doi = {10.1088/1361-6587/ab78f3},
journal = {Plasma Physics and Controlled Fusion},
number = 4,
volume = 62,
place = {United States},
year = {2020},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Statistical Simulation of the Magnetorotational Dynamo
journal, February 2015


Shell models and the possibility of application to fusion plasmas
journal, March 2010


Local Three-dimensional Magnetohydrodynamic Simulations of Accretion Disks
journal, February 1995

  • Hawley, John F.; Gammie, Charles F.; Balbus, Steven A.
  • The Astrophysical Journal, Vol. 440
  • DOI: 10.1086/175311

Zonal flow as pattern formation
journal, October 2013

  • Parker, Jeffrey B.; Krommes, John A.
  • Physics of Plasmas, Vol. 20, Issue 10
  • DOI: 10.1063/1.4828717

Zonal-flow dynamics from a phase-space perspective
journal, December 2016

  • Ruiz, D. E.; Parker, J. B.; Shi, E. L.
  • Physics of Plasmas, Vol. 23, Issue 12
  • DOI: 10.1063/1.4971813

A 3D spectral anelastic hydrodynamic code for shearing, stratified flows
journal, November 2006


A nonlinear approach to transition in subcritical plasmas with sheared flow
journal, December 2017

  • Pringle, Chris C. T.; McMillan, Ben F.; Teaca, Bogdan
  • Physics of Plasmas, Vol. 24, Issue 12
  • DOI: 10.1063/1.4999848

Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations
journal, November 2016


Quasiparticle Approach to the Modulational Instability of Drift Waves Coupling to Zonal Flows
journal, April 2005


Plasma Edge Turbulence
journal, February 1983


Pseudo-three-dimensional turbulence in magnetized nonuniform plasma
journal, January 1978

  • Hasegawa, Akira; Mima, Kunioki
  • Physics of Fluids, Vol. 21, Issue 1
  • DOI: 10.1063/1.862083

Generalized action invariants for drift waves-zonal flow systems
journal, December 1999

  • Smolyakov, A. I.; Diamond, P. H.
  • Physics of Plasmas, Vol. 6, Issue 12
  • DOI: 10.1063/1.873725

Transition to subcritical turbulence in a tokamak plasma
journal, December 2016

  • van Wyk, F.; Highcock, E. G.; Schekochihin, A. A.
  • Journal of Plasma Physics, Vol. 82, Issue 6
  • DOI: 10.1017/S0022377816001148

On the Quantum Correction For Thermodynamic Equilibrium
journal, June 1932


The modulational instability in the extended Hasegawa-Mima equation with a finite Larmor radius
journal, December 2012

  • Gallagher, S.; Hnat, B.; Connaughton, C.
  • Physics of Plasmas, Vol. 19, Issue 12
  • DOI: 10.1063/1.4773050

Streamer and zonal flow generation from envelope modulations in drift wave turbulence
journal, September 2001


Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence
journal, December 2000


Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation
journal, May 2018


Anomalous Transport Scaling in the DIII-D Tokamak Matched by Supercomputer Simulation
journal, July 2003


Zonal flow Generation by Modulational Instability
conference, January 2012

  • Dewar, Robert L.; Abdullatif, R. F.
  • Proceedings of the COSNet/CSIRO Workshop on Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media, Frontiers in Turbulence and Coherent Structures
  • DOI: 10.1142/9789812771025_0017

Bifurcation in electrostatic resistive drift wave turbulence
journal, October 2007

  • Numata, Ryusuke; Ball, Rowena; Dewar, Robert L.
  • Physics of Plasmas, Vol. 14, Issue 10
  • DOI: 10.1063/1.2796106

Avalanchelike bursts in global gyrokinetic simulations
journal, February 2009

  • McMillan, B. F.; Jolliet, S.; Tran, T. M.
  • Physics of Plasmas, Vol. 16, Issue 2
  • DOI: 10.1063/1.3079076

Coherent nonlinear structures of drift wave turbulence modulated by zonal flows
journal, December 2001

  • Kaw, Predhiman; Singh, Raghvendra; Diamond, P. H.
  • Plasma Physics and Controlled Fusion, Vol. 44, Issue 1
  • DOI: 10.1088/0741-3335/44/1/305

Drift waves and transport
journal, April 1999


A flux-balanced fluid model for collisional plasma edge turbulence: Model derivation and basic physical features
journal, October 2018

  • Majda, Andrew J.; Qi, Di; Cerfon, Antoine J.
  • Physics of Plasmas, Vol. 25, Issue 10
  • DOI: 10.1063/1.5049389

Gyrofluid turbulence models with kinetic effects
journal, March 1993

  • Dorland, W.; Hammett, G. W.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 3
  • DOI: 10.1063/1.860934

Streamer saturation: a dynamical systems approach
journal, March 2006


On non-local energy transfer via zonal flow in the Dimits shift
journal, October 2017


Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation
journal, January 2019


Radial Spreading of Drift-Wave–Zonal-Flow Turbulence via Soliton Formation
journal, July 2009


Excitation of zonal flow by drift waves in toroidal plasmas
journal, August 2000

  • Chen, Liu; Lin, Zhihong; White, Roscoe
  • Physics of Plasmas, Vol. 7, Issue 8
  • DOI: 10.1063/1.874222

Zonal flows in plasma—a review
journal, April 2005


Simple advecting structures and the edge of chaos in subcritical tokamak plasmas
journal, December 2018

  • McMillan, Ben F.; Pringle, Chris C. T.; Teaca, Bogdan
  • Journal of Plasma Physics, Vol. 84, Issue 6
  • DOI: 10.1017/S0022377818001216

Ion-scale turbulence in MAST: anomalous transport, subcritical transitions, and comparison to BES measurements
journal, September 2017

  • van Wyk, F.; Highcock, E. G.; Field, A. R.
  • Plasma Physics and Controlled Fusion, Vol. 59, Issue 11
  • DOI: 10.1088/1361-6587/aa8484

Evolution of nonlinearly coupled drift wave-zonal flow system in a nonuniform magnetoplasma
journal, February 2010


Suppression of turbulence and transport by sheared flow
journal, January 2000


Zonostrophic Instability
journal, May 2012

  • Srinivasan, Kaushik; Young, W. R.
  • Journal of the Atmospheric Sciences, Vol. 69, Issue 5
  • DOI: 10.1175/JAS-D-11-0200.1

On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability
journal, July 2018

  • Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.
  • Physics of Plasmas, Vol. 25, Issue 7
  • DOI: 10.1063/1.5039652

Developments in the gyrofluid approach to Tokamak turbulence simulations
journal, August 1993


Hamiltonian formulation of the modified Hasegawa–Mima equation
journal, February 2014


Rossby and drift wave turbulence and zonal flows: The Charney–Hasegawa–Mima model and its extensions
journal, December 2015


Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models
journal, February 2020