AI 中文总结
研究在“低密度”伽辽金截断系统中二维湍流特性，通过在傅里叶空间采样有序和无序三元组调节各向异性等，揭示双级联，发现粒子对分离有超扩散标度，各向异性影响涡度场及扩散幅度，保留光谱相互作用维持超弹道分离。
AI 中文摘要
在一个“低密度”伽辽金截断系统中研究二维湍流特性，重点关注欧拉和拉格朗日特征。在傅里叶空间中对有序伪对数和无序的{活跃（即共振）}三元组进行采样，可调节各向异性程度和“三元组密度”，以研究其对反向能量级联和粒子对扩散的影响。尽管傅里叶空间中的网格不均匀且各向异性，但该简化模型成功捕捉了二维湍流标度律并保持了积分能量级联特性。始终揭示出经典的双级联：大尺度上的$k^{-5/3}$反向级联和小尺度上的$k^{-3}$正向级联。此外，通过角度采样控制的各向异性显著影响涡度场组织和反向能量通量效率，而系统的扩散特性对粒子对分离呈现理查森超扩散标度$\ell^2(t)\sim t^3$。规定的光谱各向异性影响拉格朗日涡扩散率，在短时间尺度上增强沿一个方向的扩散。相反，对于较长时间，粒子变得不相关，分离距离退化为经典的布朗标度$\ell^2(t)\sim t$。观察到的$t^3$对色散表明保留的光谱相互作用维持超弹道分离，而各向异性主要影响色散幅度而不改变标度。
英文摘要
Two-dimensional turbulent properties are investigated within a ``low-density'' Galerkin-truncated system, with a focus on both Eulerian and Lagrangian characteristics. In particular, an ordered pseudo-logarithmic and a disordered distribution of {active (i.e. resonant)} triads has been sampled in Fourier space, allowing for a tunable degree of anisotropy and ``triadic density'', enabling investigation into their effects on the inverse energy cascade and particle pairs diffusion. Despite the non-uniform and anisotropic mesh in the Fourier space, this reduced model successfully captures 2D turbulence scaling laws and maintains integral energy cascade properties. It consistently reveals the classical double-cascade: a $k^{-5/3}$ inverse cascade at large scales and a $k^{-3}$ direct cascade at small scales, observed across all configurations. Furthermore, while anisotropy, controlled via angular sampling, significantly impacts the vorticity field organization and the efficiency of the inverse energy flux, the system's diffusive properties exhibit a Richardson superdiffusive scaling, $\ell^2(t)\sim t^3$, for particle pair separation. The prescribed spectral anisotropy affects the Lagrangian eddy diffusivity, enhancing diffusion along one direction for short timescales. Conversely, for longer times, particles become uncorrelated, and the separation distance degenerates into the classical Brownian scaling, $\ell^2(t)\sim t$. The observed $t^3$ pair-dispersion indicates that the retained spectral interactions sustain super-ballistic separation, while anisotropy mainly affects the dispersion amplitude without modifying the scaling.
