A nonmodal analytical method to predict turbulent properties applied to the HasegawaWakatani model
Abstract
Linear eigenmode analysis often fails to describe turbulence in model systems that have nonnormal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account nonmodal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. Here, we define such a nonmodal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on crossphases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as deltafunctionlike, periodic forces that randomize the state variables once every eddy turnover time. Furthermore, we estimate the eddy turnover time to be the inverse of the least stable eigenmode frequency or growth rate, which allows for prediction without nonlinear numerical simulation. Also, we test this procedure on the 2D and 3D HasegawaWakatani model [A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)] and findmore »
 Authors:
 Univ. of California, Berkeley, CA (United States). Dept. of Physics and Astronomy; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Univ. of California, Berkeley, CA (United States). Dept. of Physics and Astronomy
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE; National Science Foundation (NSF)
 OSTI Identifier:
 1395522
 Alternate Identifier(s):
 OSTI ID: 1421181
 Report Number(s):
 LLNLJRNL733803
Journal ID: ISSN 1070664X
 Grant/Contract Number:
 AC5207NA27344; PHY1202007
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 22; Journal Issue: 1; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION; DRIFTWAVE TURBULENCE; PLASMA TURBULENCE; EDGE TURBULENCE; STABILITY; INSTABILITY; FLOW; TRANSITION
Citation Formats
Friedman, B., and Carter, T. A.. A nonmodal analytical method to predict turbulent properties applied to the HasegawaWakatani model. United States: N. p., 2015.
Web. doi:10.1063/1.4905863.
Friedman, B., & Carter, T. A.. A nonmodal analytical method to predict turbulent properties applied to the HasegawaWakatani model. United States. doi:10.1063/1.4905863.
Friedman, B., and Carter, T. A.. 2015.
"A nonmodal analytical method to predict turbulent properties applied to the HasegawaWakatani model". United States.
doi:10.1063/1.4905863. https://www.osti.gov/servlets/purl/1395522.
@article{osti_1395522,
title = {A nonmodal analytical method to predict turbulent properties applied to the HasegawaWakatani model},
author = {Friedman, B. and Carter, T. A.},
abstractNote = {Linear eigenmode analysis often fails to describe turbulence in model systems that have nonnormal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account nonmodal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. Here, we define such a nonmodal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on crossphases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as deltafunctionlike, periodic forces that randomize the state variables once every eddy turnover time. Furthermore, we estimate the eddy turnover time to be the inverse of the least stable eigenmode frequency or growth rate, which allows for prediction without nonlinear numerical simulation. Also, we test this procedure on the 2D and 3D HasegawaWakatani model [A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)] and find that the nonmodal growth rate is a good predictor of energy injection rates, especially in the strongly nonnormal, fully developed turbulence regime.},
doi = {10.1063/1.4905863},
journal = {Physics of Plasmas},
number = 1,
volume = 22,
place = {United States},
year = 2015,
month = 1
}
Web of Science

Linear eigenmode analysis often fails to describe turbulence in model systems that have nonnormal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account nonmodal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. We define such amore »

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