A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model

Friedman, B.; Carter, T. A.

doi:10.1063/1.4905863

Title: A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model

Journal Article · Thu Jan 15 00:00:00 EST 2015 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4905863· OSTI ID:1395522

Friedman, B. ^[1];

^[2]

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

Linear eigenmode analysis often fails to describe turbulence in model systems that have non-normal 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 non-modal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. Here, we define such a non-modal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on cross-phases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as delta-function-like, 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 Hasegawa-Wakatani model [A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)] and find that the non-modal growth rate is a good predictor of energy injection rates, especially in the strongly non-normal, fully developed turbulence regime.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: AC52-07NA27344; PHY-1202007

OSTI ID:: 1395522

Alternate ID(s):: OSTI ID: 1421181

Report Number(s):: LLNL-JRNL-733803

Journal Information:: Physics of Plasmas, Vol. 22, Issue 1; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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The collisional drift wave instability in steep density gradient regimes Held, M.; Wiesenberger, M.; Kendl, A. Nuclear Fusion, Vol. 59, Issue 2 https://doi.org/10.1088/1741-4326/aaf6cc	journal	January 2019
Simple advecting structures and the edge of chaos in subcritical tokamak plasmas McMillan, Ben F.; Pringle, Chris C. T.; Teaca, Bogdan arXiv https://doi.org/10.48550/arxiv.1802.08519	text	January 2018

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