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.
- 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}
}