On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows

Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.

doi:10.1063/1.5038859

On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows

Journal Article · Mon Aug 27 00:00:00 EDT 2018 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5038859· OSTI ID:1467162

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Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

This study reports the stability conditions for intense zonal flows (ZFs) and the growth rate γ_TI of the corresponding “tertiary” instability (TI) within the generalized Hasegawa–Mima plasma model. The analytical calculation extends and revises Kuo's analysis of the mathematically similar barotropic vorticity equation for incompressible neutral fluids on a rotating sphere [H.-L. Kuo, J. Meteor. 6, 105 (1949)]; then, the results are applied to the plasma case. An error in Kuo's original result is pointed out. An explicit analytical formula for γ_TI is derived and compared with numerical calculations. It is shown that, within the generalized Hasegawa–Mima model, a sinusoidal ZF is TI-unstable if and only if it satisfies the Rayleigh–Kuo criterion (known from geophysics) and that the ZF wave number exceeds the inverse ion sound radius. For non-sinusoidal ZFs, the results are qualitatively similar. As a corollary, there is no TI in the geometrical-optics limit, i.e., when the perturbation wavelength is small compared to the ZF scale. Finally, this also means that the traditional wave kinetic equation, which is derived under the geometrical-optics assumption, cannot adequately describe the ZF stability.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1467162

Alternate ID(s):: OSTI ID: 1466870

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 8 Vol. 25; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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On The Rayleigh--Kuo Criterion For The Tertiary Instability Of Zonal Flows [Supplementary Data] Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y. Zenodo-Supplementary information for journal article at DOI: 10.1063/1.5038859, 5 files (12.2 kB) https://doi.org/10.5281/zenodo.1241546	dataset	May 2018
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