发表机构
University of São Paulo（圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文对比两种分数阶拉普拉斯湍流耗散模型，指出其普适类不同，并通过有效谱阶及二维极限分析，揭示涡拉伸关闭时匹配机制失效，留下开放实验问题。
AI 中文摘要
相隔二十年的两次独立尝试，都试图用分数阶拉普拉斯算子来编码湍流耗散，两者均收敛于算子阶数作为充分发展的惯性区标志：即加性的固定阶模型，以及自适应分数阶纳维-斯托克斯（AFNS）中动态变形的算子。我们表明，尽管共享这一不动点，这两种构造属于不同的普适类：Chen算子是两个固定阶核的叠加，其相对权重随尺度漂移，而AFNS则假定一个单一算子，其阶数本身随局部雷诺数连续流动。我们推导出一个尺度分辨的可观测量，即有效谱阶，其对数反常项原则上可区分这两种机制，然后从二维、涡量守恒极限中获得一个更锐利的纯解析结论：一旦运动学上关闭涡拉伸，将稳定过程指数与经验对扩散律匹配的生成机制便无解。这种二分法是否在真实的准二维流动中留下残余特征，仍是一个开放的实验挑战。
英文摘要
Two independent attempts, separated by two decades, to encode turbulent dissipation with a fractional Laplacian both converge on the operator order as the signature of the fully developedinertial range: the additive, fixed order model, and the dynamically deforming operator of the Adaptive Fractional Navier Stokes. We show that, despite sharing this fixed point, the two constructions belongto distinct universality classes: Chen operator is a superposition of two fixed order kernels whose relative weight drifts with scale, while AFNS posits a single operator whose order itself flows continuously with the local Reynolds number. We derive a scale resolved observable, the effective spectral order, whose logarithmic anomaly term discriminates between these two mechanisms in principle, and then obtain a sharper, purely analytic verdict from the two dimensional, enstrophy conserving limit: the generative mechanism matching a stable process index to the empirical pair dispersion law has no solution once vortex stretching is kinematically switched off. Whether this dichotomy leaves a residual signature in real quasi two dimensional flows is left as an open experimental challenge.
