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

Title: Another look at zonal flows: Resonance, shearing, and frictionless saturation

Abstract

We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as LZF~f3/16(1-$f$)1/8ρ $$^{5/8}_s$$ $$l^{3/8}_0$$in the (relevant) adiabatic limit (i.e., τckk$$2\atop{||}$$ D||$$\gg$$1). $f$ is the fraction of turbulence energy coupled to ZF and l0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E~(γLc)2, which indicates the extent of the “near-marginal” regime to be γLc, for the case of avalanche-induced profile variability. Here, εc is the rate of dissipation of potential enstrophy and γL is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γL are discussed.

Authors:
ORCiD logo [1];  [1]
  1. Univ. of California, San Diego, CA (United States). Center for Astrophysics & Space Sciences (CASS)
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1540198
Alternate Identifier(s):
OSTI ID: 1434357
Grant/Contract Number:  
FG02-04ER54738
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 4; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics

Citation Formats

Li, J. C., and Diamond, P. H. Another look at zonal flows: Resonance, shearing, and frictionless saturation. United States: N. p., 2018. Web. doi:10.1063/1.5027107.
Li, J. C., & Diamond, P. H. Another look at zonal flows: Resonance, shearing, and frictionless saturation. United States. doi:10.1063/1.5027107.
Li, J. C., and Diamond, P. H. Mon . "Another look at zonal flows: Resonance, shearing, and frictionless saturation". United States. doi:10.1063/1.5027107. https://www.osti.gov/servlets/purl/1540198.
@article{osti_1540198,
title = {Another look at zonal flows: Resonance, shearing, and frictionless saturation},
author = {Li, J. C. and Diamond, P. H.},
abstractNote = {We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as LZF~f3/16(1-$f$)1/8ρ $^{5/8}_s$ $l^{3/8}_0$in the (relevant) adiabatic limit (i.e., τckk$2\atop{||}$ D||$\gg$1). $f$ is the fraction of turbulence energy coupled to ZF and l0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E~(γL/εc)2, which indicates the extent of the “near-marginal” regime to be γLc, for the case of avalanche-induced profile variability. Here, εc is the rate of dissipation of potential enstrophy and γL is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γL are discussed.},
doi = {10.1063/1.5027107},
journal = {Physics of Plasmas},
number = 4,
volume = 25,
place = {United States},
year = {2018},
month = {4}
}

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

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Theory of shear flow effects on long‐wavelength drift wave turbulence
journal, October 1992

  • Carreras, B. A.; Sidikman, K.; Diamond, P. H.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 10
  • DOI: 10.1063/1.860420

Theory of drift‐acoustic instabilities in the presence of sheared flows
journal, August 1992

  • Waelbroeck, F. L.; Antonsen, T. M.; Guzdar, P. N.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 8
  • DOI: 10.1063/1.860469

Direct identification of predator-prey dynamics in gyrokinetic simulations
journal, September 2015

  • Kobayashi, Sumire; Gürcan, Özgür D.; Diamond, Patrick H.
  • Physics of Plasmas, Vol. 22, Issue 9
  • DOI: 10.1063/1.4930127

Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks
journal, July 1996


Stability of ion‐temperature‐gradient‐driven modes in the presence of sheared poloidal flows
journal, August 1992

  • Wang, X. ‐H.; Diamond, P. H.; Rosenbluth, M. N.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 8
  • DOI: 10.1063/1.860209

Zonal flows and pattern formation
journal, July 2015


Eddy Motion in the Atmosphere
journal, January 1915

  • Taylor, G. I.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 215, Issue 523-537
  • DOI: 10.1098/rsta.1915.0001

Dynamics of zonal flow saturation in strong collisionless drift wave turbulence
journal, November 2002

  • Kim, Eun-jin; Diamond, P. H.
  • Physics of Plasmas, Vol. 9, Issue 11
  • DOI: 10.1063/1.1514641

How electron two-stream instability drives cyclic Langmuir collapse and continuous coherent emission
journal, January 2017

  • Che, Haihong; Goldstein, Melvyn L.; Diamond, Patrick H.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 7
  • DOI: 10.1073/pnas.1614055114

A Key to Improved Ion Core Confinement in the JET Tokamak: Ion Stiffness Mitigation due to Combined Plasma Rotation and Low Magnetic Shear
journal, September 2011


On the validity of the local diffusive paradigm in turbulent plasma transport
journal, August 2010


How mesoscopic staircases condense to macroscopic barriers in confined plasma turbulence
journal, November 2016


Zonal Flow Patterns: How Toroidal Coupling Induces Phase Jumps and Shear Layers
journal, September 2016


Theory of mean poloidal flow generation by turbulence
journal, July 1991

  • Diamond, P. H.; Kim, Y. ‐B.
  • Physics of Fluids B: Plasma Physics, Vol. 3, Issue 7
  • DOI: 10.1063/1.859681

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


On the emergence of macroscopic transport barriers from staircase structures
journal, January 2017

  • Ashourvan, Arash; Diamond, P. H.
  • Physics of Plasmas, Vol. 24, Issue 1
  • DOI: 10.1063/1.4973660

Generation of a Sheared Plasma Rotation by Emission, Propagation, and Absorption of Drift Wave Packets
journal, July 2011


Small scale coherent vortex generation in drift wave-zonal flow turbulence
journal, December 2015

  • Guo, Z. B.; Hahm, T. S.; Diamond, P. H.
  • Physics of Plasmas, Vol. 22, Issue 12
  • DOI: 10.1063/1.4938044

The dynamics of marginality and self‐organized criticality as a paradigm for turbulent transport
journal, May 1996

  • Newman, D. E.; Carreras, B. A.; Diamond, P. H.
  • Physics of Plasmas, Vol. 3, Issue 5
  • DOI: 10.1063/1.871681

Spontaneous profile self-organization in a simple realization of drift-wave turbulence
journal, March 2016

  • Cui, L.; Ashourvan, A.; Thakur, S. C.
  • Physics of Plasmas, Vol. 23, Issue 5
  • DOI: 10.1063/1.4944819

Zonal flows in plasma—a review
journal, April 2005


Influence of sheared poloidal rotation on edge turbulence
journal, January 1990

  • Biglari, H.; Diamond, P. H.; Terry, P. W.
  • Physics of Fluids B: Plasma Physics, Vol. 2, Issue 1
  • DOI: 10.1063/1.859529

Self-Regulating Shear Flow Turbulence: A Paradigm for the L to H Transition
journal, April 1994


Non-dimensional scaling of turbulence characteristics and turbulent diffusivity
journal, September 2001


Weak Turbulence Theory of Velocity Space Diffusion and the Nonlinear Landau Damping of Waves
journal, January 1968


    Works referencing / citing this record:

    Generation of parasitic axial flow by drift wave turbulence with broken symmetry: Theory and experiment
    journal, May 2018

    • Hong, R.; Li, J. C.; Hajjar, R.
    • Physics of Plasmas, Vol. 25, Issue 5
    • DOI: 10.1063/1.5017884

    How shear increments affect the flow production branching ratio in CSDX
    journal, June 2018

    • Li, J. C.; Diamond, P. H.
    • Physics of Plasmas, Vol. 25, Issue 6
    • DOI: 10.1063/1.5033911

    On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows
    journal, August 2018

    • Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.
    • Physics of Plasmas, Vol. 25, Issue 8
    • DOI: 10.1063/1.5038859

    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