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

Zhu, Hongxuan ; Zhou, Yao ; Dodin, I. Y.
Issue date: 2020
Rights:
Creative Commons Attribution 4.0 International (CC BY)
Cite as:
Zhu, Hongxuan, Zhou, Yao, & Dodin, I. Y. Theory of the tertiary instability and the Dimits shift from reduced drift-wave models [Data set]. Princeton Plasma Physics Laboratory, Princeton University. https://doi.org/10.11578/1608302
@electronic{zhu_hongxuan_unknown,
  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}},
  url         = {https://doi.org/10.11578/1608302}
}
Description:

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.

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# Filename Filesize
1 README.txt 399 Bytes
2 ARK_DATA.zip 1.34 MB