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Title: Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics

Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. Furthermore, we find that CE2-GO retains some similarities to QL.
Authors:
ORCiD logo [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Report Number(s):
LLNL-JRNL-742576
Journal ID: ISSN 1070-664X; 897424
Grant/Contract Number:
AC52-07NA27344
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 5; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
OSTI Identifier:
1466924
Alternate Identifier(s):
OSTI ID: 1427890

Parker, Jeffrey B. Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics. United States: N. p., Web. doi:10.1063/1.5018142.
Parker, Jeffrey B. Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics. United States. doi:10.1063/1.5018142.
Parker, Jeffrey B. 2018. "Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics". United States. doi:10.1063/1.5018142.
@article{osti_1466924,
title = {Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics},
author = {Parker, Jeffrey B.},
abstractNote = {Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. Furthermore, we find that CE2-GO retains some similarities to QL.},
doi = {10.1063/1.5018142},
journal = {Physics of Plasmas},
number = 5,
volume = 25,
place = {United States},
year = {2018},
month = {3}
}