Contrasting Eulerian and Lagrangian organization of turbulent dissipation
Abstract
The dissipation of turbulent kinetic energy is conventionally attributed to a scale-invariant spatial multiplicative cascade, with Lagrangian statistics inferred through bridge relations. Direct numerical simulations with tracers reveal instead that Eulerian coarse-grained dissipation has a squared-logarithmic cascade depth and scale-dependent multipliers, whereas time-averaged dissipation along trajectories displays multifractal scaling and an approximately scale-invariant temporal cascade. The classical bridge fails at the level of individual trajectories. Eulerian multipliers nevertheless possess a multifractal organization whose accumulation accounts for the squared-logarithmic spatial statistics. This contrast motivates a material-inheritance picture in which Eulerian dissipation statistics reflect the spatial assembly, deformation, and mixing of distinct Lagrangian histories. The results therefore distinguish the temporal cascade organization revealed along fluid trajectories from the non-stationary spatial refinement observed in the Eulerian frame.
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BibTeX
@misc{bec2026contrasting,
title = {{Contrasting Eulerian and Lagrangian organization of turbulent dissipation}},
author = {Jeremie Bec and Ritwik Mukherjee and Siddhartha Mukherjee and Samriddhi Sankar Ray},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03029},
eprint = {2611.03029},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03029},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Contrasting Eulerian and Lagrangian organization of turbulent dissipation
AU - Jeremie Bec
AU - Ritwik Mukherjee
AU - Siddhartha Mukherjee
AU - Samriddhi Sankar Ray
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03029
UR - https://arxiv.org/abs/2611.03029
AB - The dissipation of turbulent kinetic energy is conventionally attributed to a scale-invariant spatial multiplicative cascade, with Lagrangian statistics inferred through bridge relations. Direct numerical simulations with tracers reveal instead that Eulerian coarse-grained dissipation has a squared-logarithmic cascade depth and scale-dependent multipliers, whereas time-averaged dissipation along trajectories displays multifractal scaling and an approximately scale-invariant temporal cascade. The classical bridge fails at the level of individual trajectories. Eulerian multipliers nevertheless possess a multifractal organization whose accumulation accounts for the squared-logarithmic spatial statistics. This contrast motivates a material-inheritance picture in which Eulerian dissipation statistics reflect the spatial assembly, deformation, and mixing of distinct Lagrangian histories. The results therefore distinguish the temporal cascade organization revealed along fluid trajectories from the non-stationary spatial refinement observed in the Eulerian frame.
ER -