Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation

Zhu, Hongxuan; Zhou, Yao; Ruiz, D. E.; Dodin, I. Y.

doi:10.1103/PhysRevE.97.053210

Title: Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation

Journal Article · Tue May 29 00:00:00 EDT 2018 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.97.053210· OSTI ID:1440782

Zhu, Hongxuan ^[1]; Zhou, Yao ^[2]; Ruiz, D. E. ^[3]; Dodin, I. Y. ^[1]

Princeton Univ., Princeton, NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact. This effective plasma can be described by a Wigner-Moyal equation (WME), which generalizes the quasilinear wave-kinetic equation (WKE) to the full-wave regime, i.e., resolves the wavelength scale. Unlike waves governed by manifestly quantumlike equations, whose WMEs can be borrowed from quantum mechanics and are commonly known, drift waves have Hamiltonians very different from those of conventional quantum particles. This causes unusual phase-space dynamics that is typically not captured by the WKE. We demonstrate how to correctly model this dynamics with the WME instead. Specifically, we report full-wave phase-space simulations of the zonal-flow formation (zonostrophic instability), deterioration (tertiary instability), and the so-called predator-prey oscillations. We also show how the WME facilitates analysis of these phenomena, namely, (i) we show that full-wave effects critically affect the zonostrophic instability, particularly its nonlinear stage and saturation; (ii) we derive the tertiary-instability growth rate; and (iii) we demonstrate that, with full-wave effects retained, the predator-prey oscillations do not require zonal-flow collisional damping, contrary to previous studies. In conclusion, we also show how the famous Rayleigh-Kuo criterion, which has been missing in wave-kinetic theories of drift-wave turbulence, emerges from the WME.

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Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466; NA0003525

OSTI ID:: 1440782

Alternate ID(s):: OSTI ID: 1439383

Journal Information:: Physical Review E, Vol. 97, Issue 5; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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References (52)

Noncurvature-driven modes in a transport barrier Rogers, B. N.; Dorland, W. Physics of Plasmas, Vol. 12, Issue 6 https://doi.org/10.1063/1.1928250	journal	June 2005
Numerical Investigation of the Instability and Nonlinear Evolution of Narrow-Band Directional Ocean Waves Eliasson, Bengt; Shukla, P. K. Physical Review Letters, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevLett.105.014501	journal	June 2010
Spatio-temporal evolution of the L → I → H transition Miki, K.; Diamond, P. H.; Gürcan, Ö. D. Physics of Plasmas, Vol. 19, Issue 9 https://doi.org/10.1063/1.4753931	journal	September 2012
Zonal-flow dynamics from a phase-space perspective Ruiz, D. E.; Parker, J. B.; Shi, E. L. Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4971813	journal	December 2016
Zonal flow as pattern formation Parker, Jeffrey B.; Krommes, John A. Physics of Plasmas, Vol. 20, Issue 10 https://doi.org/10.1063/1.4828717	journal	October 2013
Interactions of disparate scales in drift-wave turbulence Krommes, John A.; Kim, Chang-Bae Physical Review E, Vol. 62, Issue 6 https://doi.org/10.1103/PhysRevE.62.8508	journal	December 2000
Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations Parker, Jeffrey B. Journal of Plasma Physics, Vol. 82, Issue 6 https://doi.org/10.1017/S0022377816001021	journal	November 2016
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. Journal of Plasma Physics, Vol. 83, Issue 3 https://doi.org/10.1017/S002237781700037X	journal	May 2017
Dynamics of zonal flow saturation in strong collisionless drift wave turbulence Kim, Eun-jin; Diamond, P. H. Physics of Plasmas, Vol. 9, Issue 11 https://doi.org/10.1063/1.1514641	journal	November 2002
Quasiparticle Approach to the Modulational Instability of Drift Waves Coupling to Zonal Flows Trines, R.; Bingham, R.; Silva, L. O. Physical Review Letters, Vol. 94, Issue 16 https://doi.org/10.1103/PhysRevLett.94.165002	journal	April 2005
Mathematical basis for analysis of partially coherent wave propagation in nonlinear, non-instantaneous, Kerr media Semenov, V.; Lisak, M.; Anderson, D. Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 33 https://doi.org/10.1088/1751-8113/41/33/335207	journal	July 2008
Scalar Wigner theory for polarized light in nonlinear Kerr media Hansson, Tobias; Wallin, Erik; Brodin, Gert Journal of the Optical Society of America B, Vol. 30, Issue 6 https://doi.org/10.1364/JOSAB.30.001765	journal	January 2013
Coherent Structure Phenomena in Drift Wave–Zonal Flow Turbulence Smolyakov, A. I.; Diamond, P. H.; Malkov, M. Physical Review Letters, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevLett.84.491	journal	January 2000
Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics Picozzi, A.; Garnier, J.; Hansson, T. Physics Reports, Vol. 542, Issue 1 https://doi.org/10.1016/j.physrep.2014.03.002	journal	September 2014
On the stability of drift wave spectra with respect to zonal flow excitation Malkov, M. A.; Diamond, P. H.; Smolyakov, A. Physics of Plasmas, Vol. 8, Issue 5 https://doi.org/10.1063/1.1330204	journal	May 2001
Coherent structures in ion temperature gradient turbulence-zonal flow Singh, Rameswar; Singh, R.; Kaw, P. Physics of Plasmas, Vol. 21, Issue 10 https://doi.org/10.1063/1.4898207	journal	October 2014
Generalized action invariants for drift waves-zonal flow systems Smolyakov, A. I.; Diamond, P. H. Physics of Plasmas, Vol. 6, Issue 12 https://doi.org/10.1063/1.873725	journal	December 1999
Generation of zonal flows through symmetry breaking of statistical homogeneity Parker, Jeffrey B.; Krommes, John A. New Journal of Physics, Vol. 16, Issue 3 https://doi.org/10.1088/1367-2630/16/3/035006	journal	March 2014
Quantum mechanics as a statistical theory Moyal, J. E. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 45, Issue 1 https://doi.org/10.1017/S0305004100000487	journal	January 1949
Identification of Zonal Flows in a Toroidal Plasma Fujisawa, A.; Itoh, K.; Iguchi, H. Physical Review Letters, Vol. 93, Issue 16 https://doi.org/10.1103/PhysRevLett.93.165002	journal	October 2004
Landau damping and coherent structures in narrow-banded $1 + 1$ deep water gravity waves Onorato, Miguel; Osborne, Alfred; Fedele, Renato Physical Review E, Vol. 67, Issue 4 https://doi.org/10.1103/PhysRevE.67.046305	journal	April 2003
Detection of Zero-Mean-Frequency Zonal Flows in the Core of a High-Temperature Tokamak Plasma Gupta, D. K.; Fonck, R. J.; McKee, G. R. Physical Review Letters, Vol. 97, Issue 12 https://doi.org/10.1103/PhysRevLett.97.125002	journal	September 2006
A review of zonal flow experiments Fujisawa, Akihide Nuclear Fusion, Vol. 49, Issue 1 https://doi.org/10.1088/0029-5515/49/1/013001	journal	December 2008
On the Quantum Correction For Thermodynamic Equilibrium Wigner, E. Physical Review, Vol. 40, Issue 5 https://doi.org/10.1103/PhysRev.40.749	journal	June 1932
Integrability and Conservation Laws for the Nonlinear Evolution Equations of Partially Coherent Waves in Noninstantaneous Kerr Media Hansson, T.; Lisak, M.; Anderson, D. Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.063901	journal	February 2012
Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence Rogers, B. N.; Dorland, W.; Kotschenreuther, M. Physical Review Letters, Vol. 85, Issue 25 https://doi.org/10.1103/PhysRevLett.85.5336	journal	December 2000
Bifurcation in electrostatic resistive drift wave turbulence Numata, Ryusuke; Ball, Rowena; Dewar, Robert L. Physics of Plasmas, Vol. 14, Issue 10 https://doi.org/10.1063/1.2796106	journal	October 2007
Coherent nonlinear structures of drift wave turbulence modulated by zonal flows Kaw, Predhiman; Singh, Raghvendra; Diamond, P. H. Plasma Physics and Controlled Fusion, Vol. 44, Issue 1 https://doi.org/10.1088/0741-3335/44/1/305	journal	December 2001
On non-local energy transfer via zonal flow in the Dimits shift St-Onge, Denis A. Journal of Plasma Physics, Vol. 83, Issue 5 https://doi.org/10.1017/S0022377817000708	journal	October 2017
Statistical theory for incoherent light propagation in nonlinear media Hall, B.; Lisak, M.; Anderson, D. Physical Review E, Vol. 65, Issue 3 https://doi.org/10.1103/PhysRevE.65.035602	journal	February 2002
An analytic model for limiting high density LH transition by the onset of the tertiary instability Singh, Raghvendra; Jhang, Hogun; Kaang, Helen H. Physics of Plasmas, Vol. 23, Issue 7 https://doi.org/10.1063/1.4958646	journal	July 2016
Zonal flows in plasma—a review Diamond, P. H.; Itoh, S-I; Itoh, K. Plasma Physics and Controlled Fusion, Vol. 47, Issue 5 https://doi.org/10.1088/0741-3335/47/5/R01	journal	April 2005
Zonal flow generation by parametric instability in magnetized plasmas and geostrophic fluids Smolyakov, A. I.; Diamond, P. H.; Shevchenko, V. I. Physics of Plasmas, Vol. 7, Issue 5 https://doi.org/10.1063/1.873950	journal	May 2000
Wigner-Moyal description of free variable mass Klein-Gordon fields Santos, J. P.; Silva, L. O. Journal of Mathematical Physics, Vol. 46, Issue 10 https://doi.org/10.1063/1.2049169	journal	October 2005
Zonostrophic Instability Srinivasan, Kaushik; Young, W. R. Journal of the Atmospheric Sciences, Vol. 69, Issue 5 https://doi.org/10.1175/JAS-D-11-0200.1	journal	May 2012
Stationary Zonal Flows during the Formation of the Edge Transport Barrier in the JET Tokamak Hillesheim, J. C.; Delabie, E.; Meyer, H. Physical Review Letters, Vol. 116, Issue 6 https://doi.org/10.1103/PhysRevLett.116.065002	journal	February 2016
Developments in the gyrofluid approach to Tokamak turbulence simulations Hammett, G. W.; Beer, M. A.; Dorland, W. Plasma Physics and Controlled Fusion, Vol. 35, Issue 8 https://doi.org/10.1088/0741-3335/35/8/006	journal	August 1993
Rossby and drift wave turbulence and zonal flows: The Charney–Hasegawa–Mima model and its extensions Connaughton, Colm; Nazarenko, Sergey; Quinn, Brenda Physics Reports, Vol. 604 https://doi.org/10.1016/j.physrep.2015.10.009	journal	December 2015
Self-Regulating Shear Flow Turbulence: A Paradigm for the L to H Transition Diamond, P. H.; Liang, Y. -M.; Carreras, B. A. Physical Review Letters, Vol. 72, Issue 16 https://doi.org/10.1103/PhysRevLett.72.2565	journal	April 1994
Zonal Flows and Transient Dynamics of the $L − H$ Transition Kim, Eun-jin; Diamond, P. H. Physical Review Letters, Vol. 90, Issue 18 https://doi.org/10.1103/PhysRevLett.90.185006	journal	May 2003
White-Light Parametric Instabilities in Plasmas Santos, J. E.; Silva, L. O.; Bingham, R. Physical Review Letters, Vol. 98, Issue 23 https://doi.org/10.1103/PhysRevLett.98.235001	journal	June 2007
Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence Constantinou, Navid C.; Farrell, Brian F.; Ioannou, Petros J. Journal of the Atmospheric Sciences, Vol. 73, Issue 5 https://doi.org/10.1175/JAS-D-15-0288.1	journal	May 2016
White-light parametric instabilities in plasmas Santos, J. E.; Silva, L. O.; Bingham, R. arXiv https://doi.org/10.48550/arxiv.0704.2831	text	January 2007
Bifurcation in electrostatic resistive drift wave turbulence Numata, Ryusuke; Ball, Rowena; Dewar, Robert L. arXiv https://doi.org/10.48550/arxiv.0708.4317	text	January 2007
A Scalar Wigner Theory for Polarized Light in Nonlinear Kerr Media Hansson, T.; Wallin, E.; Brodin, G. arXiv https://doi.org/10.48550/arxiv.1210.7107	text	January 2012
Zonal Flow as Pattern Formation Parker, Jeffrey B.; Krommes, John A. arXiv https://doi.org/10.48550/arxiv.1301.5059	text	January 2013
Rossby and Drift Wave Turbulence and Zonal Flows: the Charney-Hasegawa-Mima model and its extensions Connaughton, Colm; Nazarenko, Sergey; Quinn, Brenda arXiv https://doi.org/10.48550/arxiv.1407.1896	text	January 2014
Statistical state dynamics of jet/wave coexistence in barotropic beta-plane turbulence Constantinou, Navid C.; Farrell, Brian F.; Ioannou, Petros J. arXiv https://doi.org/10.48550/arxiv.1509.06326	text	January 2015
Dynamics of Zonal Flows: Failure of Wave-Kinetic Theory, and New Geometrical Optics Approximations Parker, Jeffrey B. arXiv https://doi.org/10.48550/arxiv.1604.06904	text	January 2016
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. arXiv https://doi.org/10.48550/arxiv.1702.03052	text	January 2017
On Nonlocal Energy Transfer via Zonal Flow in the Dimits Shift St-Onge, Denis A. arXiv https://doi.org/10.48550/arxiv.1704.05406	text	January 2017
Generalized Action Invariants for Drift Waves-Zonal Flow Systems Smolyakov, A. I.; Diamond, P. H. arXiv https://doi.org/10.48550/arxiv.physics/9910018	text	January 1999

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