A closer look at turbulence spreading: How bistability admits intermittent, propagating turbulence fronts

doi:https://doi.org/10.1063/1.5138129

Title: A closer look at turbulence spreading: How bistability admits intermittent, propagating turbulence fronts

Abstract

In magnetic fusion plasmas, mounting evidence indicates the possibility of sustained turbulence below the linear stability threshold or more generally global turbulence bistability. The usual reduced models for turbulence spreading are unistable/supercritical and incompatible with this result. The older models further cannot realistically support fronts connecting laminar and turbulent domains. In this work, a minimal model for “subcritical” turbulence spreading is introduced and analyzed. The model may be viewed as phenomenological or derived directly by considering the effect of profile corrugations in an E×B staircase. The model, which is related to the FitzHugh–Nagumo system, supports the robust coexistence of multiple turbulence levels via bistability. We show that this model predicts stronger penetration of turbulence into a linearly stable region as well as the formation of intermittent turbulence fronts that resemble avalanches. We derive the critical size that a localized slug of turbulence must exceed in order to spread. Lastly, we make a prediction of global hysteretic behavior associated with the bistability, which should be testable via experiment.

Authors:

^[1];

^[1]

Univ. of California, San Diego, CA (United States)

Publication Date:: 2020-03-05

Research Org.:: Univ. of California, San Diego, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

OSTI Identifier:: 1603366

Alternate Identifier(s):: OSTI ID: 1603189

Grant/Contract Number:: FG02-04ER54738

Resource Type:: Journal Article: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 27; Journal Issue: 3; 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

Citation Formats


                    Heinonen, Robin A., and Diamond, P. H. A closer look at turbulence spreading: How bistability admits intermittent, propagating turbulence fronts.  United States: N. p., 2020. 
        Web.  doi:10.1063/1.5138129.

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                    Heinonen, Robin A., & Diamond, P. H. A closer look at turbulence spreading: How bistability admits intermittent, propagating turbulence fronts.  United States.  https://doi.org/10.1063/1.5138129

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                    Heinonen, Robin A., and Diamond, P. H. Thu .  
        "A closer look at turbulence spreading: How bistability admits intermittent, propagating turbulence fronts".  United States.  https://doi.org/10.1063/1.5138129.  https://www.osti.gov/servlets/purl/1603366.

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@article{osti_1603366,

  title        = {A closer look at turbulence spreading: How bistability admits intermittent, propagating turbulence fronts},

  author       = {Heinonen, Robin A. and Diamond, P. H.},

  abstractNote = {In magnetic fusion plasmas, mounting evidence indicates the possibility of sustained turbulence below the linear stability threshold or more generally global turbulence bistability. The usual reduced models for turbulence spreading are unistable/supercritical and incompatible with this result. The older models further cannot realistically support fronts connecting laminar and turbulent domains. In this work, a minimal model for “subcritical” turbulence spreading is introduced and analyzed. The model may be viewed as phenomenological or derived directly by considering the effect of profile corrugations in an E×B staircase. The model, which is related to the FitzHugh–Nagumo system, supports the robust coexistence of multiple turbulence levels via bistability. We show that this model predicts stronger penetration of turbulence into a linearly stable region as well as the formation of intermittent turbulence fronts that resemble avalanches. We derive the critical size that a localized slug of turbulence must exceed in order to spread. Lastly, we make a prediction of global hysteretic behavior associated with the bistability, which should be testable via experiment.},

  doi          = {10.1063/1.5138129},

  url          = {https://www.osti.gov/biblio/1603366},
  journal      = {Physics of Plasmas},

  issn         = {1070-664X},

  number       = 3,

  volume       = 27,

  place        = {United States},

  year         = {2020},

  month        = {3}

}

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Title: A closer look at turbulence spreading: How bistability admits intermittent, propagating turbulence fronts

Abstract

Citation Formats

Mesoscopic Transport Events and the Breakdown of Fick’s Law for Turbulent Fluxes journal, September 2018

Turbulent Transport in Tokamak Plasmas with Rotational Shear journal, April 2011

Finding the Elusive E × B Staircase in Magnetized Plasmas journal, February 2015

Impulses and Physiological States in Theoretical Models of Nerve Membrane journal, July 1961

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Intermittent transition to turbulence in dissipative dynamical systems journal, June 1980

How is turbulence intensity determined by macroscopic variables in a toroidal plasma? journal, September 2013

Turbulence spreading and transport scaling in global gyrokinetic particle simulations journal, March 2004

Front motion, metastability and subcritical bifurcations in hydrodynamics journal, December 1986

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

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

An Active Pulse Transmission Line Simulating Nerve Axon journal, October 1962

Non-perturbative models of intermittency in drift-wave turbulence: towards a probabilistic theory of anomalous transport journal, August 2003

Gyrokinetic simulations of off-axis minimum-q profile corrugations journal, May 2006

Wave speeds of density dependent Nagumo diffusion equations – inspired by oscillating gap-junction conductance in the islets of Langerhans journal, December 2004

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Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations journal, June 1997

The mechanism of self‐sustainment in collisional drift wave turbulence journal, August 1992

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Measurement of Turbulence Decorrelation during Transport Barrier Evolution in a High-Temperature Fusion Plasma journal, April 2005

Turbulence spreading, anomalous transport, and pinch effect journal, December 2005

Landau-Ginzburg Theory of Self-Organized Criticality journal, May 1996

Zonal flows in plasma—a review journal, April 2005

Suppression of shear damping in drift wave turbulence journal, May 1985

Intermittent particle transport in two-dimensional edge turbulence journal, December 1998

Self-sustained collisional drift-wave turbulence in a sheared magnetic field journal, December 1990

Effects of q-profile structure on turbulence spreading: A fluctuation intensity transport analysis journal, September 2014

The transition to turbulence in parallel flows: A personal view journal, March 2015

Ballistic propagation of turbulence front in tokamak edge plasmas journal, October 2012

Nonlinear Self-Sustained Drift-Wave Turbulence journal, December 1995

Dynamics of turbulence spreading in magnetically confined plasmas journal, March 2005

Some exact solutions to a non-linear diffusion problem in population genetics and combustion journal, July 1980

Mesoscopic Transport Events and the Breakdown of Fick’s Law for Turbulent Fluxes
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Turbulent Transport in Tokamak Plasmas with Rotational Shear
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Finding the Elusive $E \times B$ Staircase in Magnetized Plasmas
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Impulses and Physiological States in Theoretical Models of Nerve Membrane
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The rise of fully turbulent flow
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Intermittent transition to turbulence in dissipative dynamical systems
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How is turbulence intensity determined by macroscopic variables in a toroidal plasma?
journal, September 2013

Turbulence spreading and transport scaling in global gyrokinetic particle simulations
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Front motion, metastability and subcritical bifurcations in hydrodynamics
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On the validity of the local diffusive paradigm in turbulent plasma transport
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An Active Pulse Transmission Line Simulating Nerve Axon
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Non-perturbative models of intermittency in drift-wave turbulence: towards a probabilistic theory of anomalous transport
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Gyrokinetic simulations of off-axis minimum-q profile corrugations
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Wave speeds of density dependent Nagumo diffusion equations – inspired by oscillating gap-junction conductance in the islets of Langerhans
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Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations
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