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 L ZF~f 3/16(1-$$f$$) 1/8ρ $$^{5/8}_s$$ $$l^{3/8}_0$$in the (relevant) adiabatic limit (i.e., τ ckk$$2\atop{||}$$ D ||$$\gg$$1). $$f$$ is the fraction of turbulence energy coupled to ZF and l 0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional,more »
- Authors:
-
- 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:
- Journal Article: 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. https://doi.org/10.1063/1.5027107
Li, J. C., and Diamond, P. H. Mon .
"Another look at zonal flows: Resonance, shearing, and frictionless saturation". United States. https://doi.org/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},
url = {https://www.osti.gov/biblio/1540198},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 4,
volume = 25,
place = {United States},
year = {2018},
month = {4}
}
Web of Science
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
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
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
Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks
journal, July 1996
- Dimits, A. M.; Williams, T. J.; Byers, J. A.
- Physical Review Letters, Vol. 77, Issue 1
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
Zonal flows and pattern formation
journal, July 2015
- Gürcan, Ö D.; Diamond, P. H.
- Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 29
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
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
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
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
- Mantica, P.; Angioni, C.; Challis, C.
- Physical Review Letters, Vol. 107, Issue 13
On the validity of the local diffusive paradigm in turbulent plasma transport
journal, August 2010
- Dif-Pradalier, G.; Diamond, P. H.; Grandgirard, V.
- Physical Review E, Vol. 82, Issue 2
How mesoscopic staircases condense to macroscopic barriers in confined plasma turbulence
journal, November 2016
- Ashourvan, Arash; Diamond, P. H.
- Physical Review E, Vol. 94, Issue 5
Zonal Flow Patterns: How Toroidal Coupling Induces Phase Jumps and Shear Layers
journal, September 2016
- Guo, Z. B.; Diamond, P. H.
- Physical Review Letters, Vol. 117, Issue 12
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
Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence
journal, December 2000
- Rogers, B. N.; Dorland, W.; Kotschenreuther, M.
- Physical Review Letters, Vol. 85, Issue 25
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
Generation of a Sheared Plasma Rotation by Emission, Propagation, and Absorption of Drift Wave Packets
journal, July 2011
- Xu, M.; Tynan, G. R.; Diamond, P. H.
- Physical Review Letters, Vol. 107, Issue 5
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
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
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
Zonal flows in plasma—a review
journal, April 2005
- Diamond, P. H.; Itoh, S-I; Itoh, K.
- Plasma Physics and Controlled Fusion, Vol. 47, Issue 5
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
Self-Regulating Shear Flow Turbulence: A Paradigm for the L to H Transition
journal, April 1994
- Diamond, P. H.; Liang, Y. -M.; Carreras, B. A.
- Physical Review Letters, Vol. 72, Issue 16
Non-dimensional scaling of turbulence characteristics and turbulent diffusivity
journal, September 2001
- McKee, G. R.; Petty, C. C.; Waltz, R. E.
- Nuclear Fusion, Vol. 41, Issue 9
Weak Turbulence Theory of Velocity Space Diffusion and the Nonlinear Landau Damping of Waves
journal, January 1968
- Manheimer, Wallace M.
- Physics of Fluids, Vol. 11, Issue 12
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
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
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
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