Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theory of the tertiary instability and the Dimits shift from reduced
  drift-wave models   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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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg