The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$ -pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations (Dimits et al., Phys. Plasmas, vol. 7, 2000, 969). A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear (van Wyk et al., J. Plasma Phys., vol. 82, 2016, 905820609). The breakup of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system – the Reynolds stress and the advection of the diamagnetic flow by the $\boldsymbol {E}\times \boldsymbol {B}$ flow. By analysing the linear ion-temperature-gradient modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

中文翻译：

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曲率驱动的 ITG 湍流中的纬向主导动力学和 Dimits 阈值

使用二维长波长流体模型研究了由离子温度梯度不稳定性驱动的饱和湍流状态，该模型描述了具有恒定曲率的磁场中的扰动静电势和扰动离子温度（a $Z$ -pinch）和平衡温度梯度。数值模拟揭示了由强纬向流动和纬向温度扰动主导的有限幅度饱和状态与在与盒无关的尺度上未能饱和的爆破状态之间的明确过渡。我们认为这种转变等同于在陀螺动力学数值模拟中看到的从低传输状态到高传输状态的 Dimits 转变（Dimits等。,物理。等离子, 卷。7, 2000, 969)。在 Dimits 阈值附近出现了温度梯度的准静态阶梯状结构，与纬向流交织在一起，具有斑块式恒定剪切。低碰撞性近边缘状态下的湍流热通量主要由湍流爆发主导，由与施加平衡流剪切的旋回动力学模拟中发现的相干长寿命结构非常相似（van Wyk）触发。等。,J.等离子物理学。, 卷。82, 2016, 905820609)。低传输 Dimits 状态的解体与系统中两种不同的极向动量源之间的竞争有关——雷诺应力和反磁流动的平流 $\boldsymbol {E}\times \boldsymbol {B}$ 流动。通过分析线性离子-温度-梯度模式，我们获得了大碰撞下Dimits阈值的半解析模型。