标量模型中的第三不稳定性和Dimits位移理论
Theory of the tertiary instability and the Dimits shift within a scalar model
摘要：
迪米特位移是磁化等离子体中漂移波初级不稳定性的阈值与湍流输运的实际开始之间的位移。它通常归因于纬向流对湍流的抑制，但要发展更详细的理解，需要考虑特定的简化模型。St-Onge [J. Plasma Phys. $\boldsymbol{\rm 83}$，905830504（2017）]提出了改进的Terry-Horton系统，作为捕获Dimits位移的极小模型。在这里，我们使用这个模型来开发的迪米特移动的分析理论和相关的理论的第三次不稳定的纬向流。我们发现，三次模的纬向速度$U(x)$，其中$x$是径向坐标的极值附近的本地化。通过近似$U(x)$与抛物线，我们得到的第三不稳定性的增长率使用两种不同的方法，并表明，第三不稳定性基本上是由本地$U''$修改的主要漂移波不稳定性。然后，根据$U''$，三级不稳定性可以被抑制或释放。前者对应于当纬向流足够强以抑制湍流（Dimits区域）时的情况，而后者对应于当纬向流不稳定并且湍流发展时的情况。这种理解不同于传统的湍流由流动剪切$U'$控制的范例。我们的分析预测与直接数值模拟的修改后的特里-霍顿系统。
英文摘要：
The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry--Horton system has been proposed by St-Onge [J. Plasma Phys. $\boldsymbol{\rm 83}$, 905830504 (2017)] as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$, where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U''$. Then, depending on $U''$, the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $U'$. Our analytic predictions are in agreement with direct numerical simulations of the modified Terry--Horton system.
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