# Theory of the tertiary instability and the Dimits shift from reduced drift-wave models

Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.
Issue date: January 2020
Cite as:
Zhu, Hongxuan, Zhou, Yao, & Dodin, I. Y. (2020). Theory of the tertiary instability and the Dimits shift from reduced drift-wave models [Data set]. Princeton Plasma Physics Laboratory, Princeton University.
@electronic{zhu_hongxuan_2020,
author      = {Zhu, Hongxuan and
Zhou, Yao and
Dodin, I. Y.},
title       = {{Theory of the tertiary instability and t
he Dimits shift from reduced drift-wave
models}},
publisher   = {{Princeton Plasma Physics Laboratory, Pri
nceton University}},
year        = 2020
}
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 $\gamma_{\rm TI}$ is derived within the modified Hasegawa--Wakatani model. We show that $\gamma_{\rm TI}$ 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.