发表机构
Laboratoire de Physique des Plasmas, CNRS, Ecole Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris（等离子体物理实验室，法国国家科学研究中心，巴黎综合理工学院，索邦大学，萨克雷大学，巴黎天文台）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二维流体ITG模型中不同非线性项与位涡守恒的作用，发现抗磁非线性项影响带状流主导性与湍能级联，通过含高阶项的四非线性模型可守恒位涡并解决相关问题。
AI 中文摘要
本文详细研究了离子温度梯度驱动湍流的简单二维流体模型的湍动能级联特性。值得注意的是，研究发现环形ITG的两场最小模型在有无抗磁非线性项时表现出显著的定性差异：无该项时，带状流始终占主导，系统永远无法达到高输运状态；相反，当包含该项时，带状流仅在边际性附近占主导，而远离边际性时，会观测到具有高输运水平的逆级联，这需要大尺度耗散（ hypoviscosity）来饱和，同时需要超粘性（hyperviscosity）来正则化与该非线性项相关的小尺度不稳定性。然而，引入该项并结合曲率项的存在会破坏位涡守恒，而位涡是漂移波湍流的关键对称性之一。这一问题可通过考虑保留压强方程中高阶项的更完整模型来解决，这种包含四个非线性项的模型可守恒位涡，且表现与原模型类似，由于新增的非线性项也会在压强方程中产生小尺度不稳定性，因此需要超粘性来饱和。为表征位涡守恒和压强方程中高阶项的作用，本文通过分析标准ITG系统和位涡守恒系统的能谱、湍能级联以及对粘性的敏感性，对两者的行为进行了研究。最后，通过考察不同非线性项（尤其是抗磁非线性项）对谱能量转移的贡献，并分别考虑每个非线性项的三重态不稳定性假设，研究了由这些非线性项引起的湍能级联方向。
英文摘要
The nature of turbulent energy cascade of simple two-dimensional fluid models of ion temperature gradient driven turbulence is studied in detail. Notably, it is observed that a minimal two-field model of toroidal ITG, behaves qualitatively differently with or without the diamagnetic nonlinearity. In its absence, the zonal flows always dominate and the system never reaches a high-transport state. In contrast, when this term is included, zonal flows dominate only near marginality, while away from it, an inverse cascade with high levels of transport is observed, requiring large-scale dissipation (hypoviscosity) to saturate and hyperviscosity to regularize small scale instability associated with this nonlinear term. However introducing such a term, together with the existence of the curvature term, breaks potential vorticity conservation, which is one of the key symmetries of drift-wave turbulence. This can be remedied by considering a more complete model that retains higher-order terms in the pressure equation. This form of the model, with four nonlinearities, conserves potential vorticity and behaves similarly to the original model, requiring hyperviscosity to saturate since the added nonlinearity generates small scale instability also for the pressure equation. To characterize the roles of potential vorticity conservation and higher-order terms in the pressure equation, the behavior of both the standard ITG system, and the potential vorticity conserving system, is studied by analyzing their spectra, turbulent cascades, and sensitivity to viscosity. Finally, the direction of turbulent cascade due to the different nonlinearities (i.e. the diamagnetic nonlinearity in particular) is investigated by examining their contributions to the spectral energy transfer and by considering the triadic instability assumption for each of these nonlinearities separately.
Comments30 pages, 17 figures
