Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01z603r1322
 Title: Theory of the tertiary instability and the Dimits shift from reduced drift-wave models Contributors: Zhu, HongxuanZhou, YaoDodin, I. Y.U. S. Department of Energy Keywords: drift-wave turbulencezonal flowstertiary instabilityDimits 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. URI: http://arks.princeton.edu/ark:/88435/dsp01z603r1322 Appears in Collections: Theory and Computation