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2 results for “zonal flows”
On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows
<p>These are the supplementary Matlab codes that can be used to generate the data in figure 3, 4, and 6 in the manuscript "On the Rayleigh--Kuo criterion for the tertiary instability of zonal flows". The abstract of this manuscript reads as follows:</p> <p>This paper reports the stability conditions for intense zonal flows (ZFs) and the growth rate $\gamma_{\rm TI}$ of the corresponding "tertiary" instability (TI) within the generalized Hasegawa--Mima plasma model. The analytic calculation extends and revises Kuo's analysis of the mathematically similar barotropic vorticity equation for incompressible neutral fluids on a rotating sphere [H.-L. Kuo, J. Meteor. 6, 105 (1949)]; then, the results are applied to the plasma case. An error in Kuo's original result is pointed out. An explicit analytic formula for $\gamma_{\rm TI}$ is derived and compared with numerical calculations. It is shown that a ZF is TI-unstable under the Rayleigh--Kuo criterion known from geophysics plus the condition that the ZF wave number must exceed the inverse ion sound radius. For a sinusoidal ZF, these two necessary conditions combined together are also sufficient for the TI. For non-sinusoidal ZFs, the results are qualitatively consistent. As a corollary, there is no TI in the geometrical-optics limit, i.e., when the DW wavelength is small compared to the ZF scale. This also means that the traditional wave kinetic equation under the geometrical-optics assumption cannot adequately describe the ZF stability.</p>
On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability
<p>These are the supplementary data that can be used to generate figure 3, 4, and 5 in the manuscript "On the structure of the drifton phase space and its relation to the Rayleigh--Kuo criterion of the zonal-flow stability". The abstract of this manuscript reads as follows:</p> <p>The phase space of driftons (drift-wave quanta) is studied within the generalized Hasegawa--Mima collisionless-plasma model in the presence of zonal flows. This phase space is made intricate by the corrections to the drifton ray equations that were recently proposed by Parker [J. Plasma Phys. 82, 595820602 (2016)] and Ruiz et al. [Phys. Plasmas 23, 122304 (2016)]. Contrary to the traditional geometrical-optics (GO) model of the drifton dynamics, it is found that driftons can be not only trapped or passing, but they can also accumulate spatially while experiencing indefinite growth of their momenta. In particular, it is found that the Rayleigh--Kuo threshold known from geophysics corresponds to the regime when such "runaway" trajectories are the only ones possible. On one hand, this analysis helps visualize the development of the zonostrophic instability, particularly its nonlinear stage, which is studied here both analytically and through wave-kinetic simulations. On the other hand, the GO theory predicts that zonal flows above the Rayleigh--Kuo threshold can only grow; hence, the deterioration of intense zonal flows cannot be captured within a GO model. In particular, this means that the so-called tertiary instability of intense zonal flows cannot be adequately described within the quasilinear wave kinetic equation, contrary to some previous studies.</p>
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