从单一拉格朗日轨迹通过隐马尔可夫切换推断多尺度级联结构
Inferring Multi-Scale Cascade Structure from a Single Lagrangian Trajectory via Hidden Markov Switching
- University of Pittsburgh（匹兹堡大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出马尔可夫切换多重分形框架，从单一拉格朗日轨迹推断多尺度级联状态，并证明其携带空间信息，为稀疏轨迹湍流诊断开辟新途径。
AI中文摘要：
我们证明，单一拉格朗日轨迹不仅编码时间级联结构，还编码空间级联结构——无需访问空间分辨的欧拉速度场即可恢复。我们报告了一个马尔可夫切换多重分形（MSM）框架，该框架直接从单粒子轨迹推断隐藏的多尺度级联状态。科尔莫戈罗夫标度固定了模型的切换速率，仅留下一个校准的间歇性参数；精确贝叶斯滤波随后返回沿轨迹的层分辨级联状态的后验分布。当我们独立地将MSM框架应用于粒子对的每条轨迹时，我们发现推断的状态携带真实的空间信息：与理查森局域性图像一致，当细尺度层被随机化时，科尔莫戈罗夫$r^{1/3}$标度得以保留，但一旦随机化跨越由粒子对间距设定的层，该标度就会崩溃。因此，单一轨迹编码了级联的空间组织，为主要通过稀疏或单个拉格朗日轨迹可访问的湍流级联诊断开辟了一条途径——从粒子跟踪测速到大气和海洋学跟踪——在这些场景中，瞬时欧拉场无法获取。
英文摘要：
We show that a single Lagrangian trajectory encodes not only temporal but also spatial cascade structure--recoverable without access to a spatially resolved Eulerian velocity field. We report a Markov-Switching Multifractal (MSM) framework that infers hidden multi-scale cascade states directly from single-particle trajectories. Kolmogorov scaling fixes the model's switching rates, leaving a single calibrated intermittency parameter; exact Bayesian filtering then returns the posterior of the layer-resolved cascade state along the trajectory. When we apply the MSM framework independently to each trajectory of a particle pair, we find that the inferred states carry genuine spatial information: consistent with Richardson's locality picture, the Kolmogorov $r^{1/3}$ scaling is preserved when fine-scale layers are randomized, but collapses once the randomization crosses the layer set by the pair separation. Single trajectories thus encode the spatial organization of the cascade, opening a route to cascade diagnostics for turbulent flows accessible primarily through sparse or individual Lagrangian trajectories--from particle-tracking velocimetry to atmospheric and oceanographic tracking--where the instantaneous Eulerian field is out of reach.
