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Title: Theory of the tertiary instability and the Dimits shift from reduced drift-wave models
Contributors: Zhu, Hongxuan
Zhou, Yao
Dodin, I. Y.
U. S. Department of Energy
Keywords: drift-wave turbulence
zonal flows
tertiary instability
Dimits shift;
Issue Date: Jan-2020
Publisher: Princeton Plasma Physics Laboratory, Princeton University
Related Publication: Physical Review Letters
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.
Appears in Collections:Theory and Computation

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