Inferring Multi-Scale Cascade Structure from a Single Lagrangian Trajectory via Hidden Markov Switching
Abstract
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 r1/3 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.
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BibTeX
@misc{yang2026inferring,
title = {{Inferring Multi-Scale Cascade Structure from a Single Lagrangian Trajectory via Hidden Markov Switching}},
author = {Ziang Yang and Lei Fang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08971},
eprint = {2610.08971},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08971},
}
RIS
TY - UNPB
TI - Inferring Multi-Scale Cascade Structure from a Single Lagrangian Trajectory via Hidden Markov Switching
AU - Ziang Yang
AU - Lei Fang
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08971
UR - https://arxiv.org/abs/2610.08971
AB - 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.
ER -