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Title: Zonal-flow dynamics from a phase-space perspective

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. But, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. Furthermore, we derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. We present numerical simulations to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.
Authors:
ORCiD logo [1] ; ORCiD logo [2] ; ORCiD logo [1] ;  [3]
  1. Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Report Number(s):
LLNL-JRNL-736306
Journal ID: ISSN 1070-664X; TRN: US1701137
Grant/Contract Number:
32- CFR-168a; NA0002948; AC52-07NA27344; AC02-09CH11466
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 12; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 70 PLASMA PHYSICS AND FUSION
OSTI Identifier:
1347105
Alternate Identifier(s):
OSTI ID: 1336500; OSTI ID: 1418955

Ruiz, D. E., Parker, J. B., Shi, E. L., and Dodin, I. Y.. Zonal-flow dynamics from a phase-space perspective. United States: N. p., Web. doi:10.1063/1.4971813.
Ruiz, D. E., Parker, J. B., Shi, E. L., & Dodin, I. Y.. Zonal-flow dynamics from a phase-space perspective. United States. doi:10.1063/1.4971813.
Ruiz, D. E., Parker, J. B., Shi, E. L., and Dodin, I. Y.. 2016. "Zonal-flow dynamics from a phase-space perspective". United States. doi:10.1063/1.4971813. https://www.osti.gov/servlets/purl/1347105.
@article{osti_1347105,
title = {Zonal-flow dynamics from a phase-space perspective},
author = {Ruiz, D. E. and Parker, J. B. and Shi, E. L. and Dodin, I. Y.},
abstractNote = {The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. But, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. Furthermore, we derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. We present numerical simulations to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.},
doi = {10.1063/1.4971813},
journal = {Physics of Plasmas},
number = 12,
volume = 23,
place = {United States},
year = {2016},
month = {12}
}