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Title: Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models

Abstract

Tertiary modes in electrostatic drift-wave turbulence are localized near extrema of the zonal velocity U(x) with respect to the radial coordinate x. We argue that these modes can be described as quantum harmonic oscillators with complex frequencies, so their spectrum can be readily calculated. The corresponding growth rate $γ$TI is derived within the modified Hasegawa-Wakatani model. We show that $γ$TI equals the primary-instability growth rate plus a term that depends on the local U''; hence, the instability threshold is shifted compared to that in homogeneous turbulence. This provides a generic explanation of the well-known yet elusive Dimits shift, which we find explicitly in the Terry-Horton limit. Linearly unstable tertiary modes either saturate due to the evolution of the zonal density or generate radially propagating structures when the shear |U'| is sufficiently weakened by viscosity. The Dimits regime ends when such structures are generated continuously.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1616941
Alternate Identifier(s):
OSTI ID: 1599479
Grant/Contract Number:  
AC02-09CH11466; EP/M022463/1; EP/R029148/
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 124; Journal Issue: 5; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Drift waves; Flow instability; Plasma transport; Shear flows; Transition to turbulence

Citation Formats

Zhu, Hongxuan, Zhou, Yao, and Dodin, I. Y. Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models. United States: N. p., 2020. Web. https://doi.org/10.1103/PhysRevLett.124.055002.
Zhu, Hongxuan, Zhou, Yao, & Dodin, I. Y. Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models. United States. https://doi.org/10.1103/PhysRevLett.124.055002
Zhu, Hongxuan, Zhou, Yao, and Dodin, I. Y. Tue . "Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models". United States. https://doi.org/10.1103/PhysRevLett.124.055002. https://www.osti.gov/servlets/purl/1616941.
@article{osti_1616941,
title = {Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models},
author = {Zhu, Hongxuan and Zhou, Yao and Dodin, I. Y.},
abstractNote = {Tertiary modes in electrostatic drift-wave turbulence are localized near extrema of the zonal velocity U(x) with respect to the radial coordinate x. We argue that these modes can be described as quantum harmonic oscillators with complex frequencies, so their spectrum can be readily calculated. The corresponding growth rate $γ$TI is derived within the modified Hasegawa-Wakatani model. We show that $γ$TI equals the primary-instability growth rate plus a term that depends on the local U''; hence, the instability threshold is shifted compared to that in homogeneous turbulence. This provides a generic explanation of the well-known yet elusive Dimits shift, which we find explicitly in the Terry-Horton limit. Linearly unstable tertiary modes either saturate due to the evolution of the zonal density or generate radially propagating structures when the shear |U'| is sufficiently weakened by viscosity. The Dimits regime ends when such structures are generated continuously.},
doi = {10.1103/PhysRevLett.124.055002},
journal = {Physical Review Letters},
number = 5,
volume = 124,
place = {United States},
year = {2020},
month = {2}
}

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