Geometric Mechanics of Real-Space Energy Transfer in Turbulence
Abstract
How the local energy transfer across scales in turbulence is encoded in the instantaneous deformation of fluid elements remains a fundamental question. We exploit the spherical geometry of the real-space energy cascade at length scale ℓ. An exact derivation shows that it can be decomposed locally by strain self-amplification and vortex stretching, with a coefficient equal to the specific moment of inertia 2/5(ℓ/2)2 of a spherical fluid neighborhood. Direct numerical simulations show that this contribution captures the dominant local transfer and defines a statistical boundary separating forward- and inverse-cascade events. A further longitudinal and transverse decomposition reveals that the longitudinal transfer underlying Kolmogorov's 4/5 law is governed solely by strain self-amplification, whereas vortex stretching enters through the transverse component. These results establish a purely mechanical connection between turbulent energy cascade and the local rotational and deformational dynamics of fluid elements.
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BibTeX
@misc{zhang2026geometric,
title = {{Geometric Mechanics of Real-Space Energy Transfer in Turbulence}},
author = {Weijie Zhang and Hanxun Yao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11029},
eprint = {2610.11029},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11029},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric Mechanics of Real-Space Energy Transfer in Turbulence
AU - Weijie Zhang
AU - Hanxun Yao
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11029
UR - https://arxiv.org/abs/2610.11029
AB - How the local energy transfer across scales in turbulence is encoded in the instantaneous deformation of fluid elements remains a fundamental question. We exploit the spherical geometry of the real-space energy cascade at length scale ℓ. An exact derivation shows that it can be decomposed locally by strain self-amplification and vortex stretching, with a coefficient equal to the specific moment of inertia 2/5(ℓ/2)^2 of a spherical fluid neighborhood. Direct numerical simulations show that this contribution captures the dominant local transfer and defines a statistical boundary separating forward- and inverse-cascade events. A further longitudinal and transverse decomposition reveals that the longitudinal transfer underlying Kolmogorov's 4/5 law is governed solely by strain self-amplification, whereas vortex stretching enters through the transverse component. These results establish a purely mechanical connection between turbulent energy cascade and the local rotational and deformational dynamics of fluid elements.
ER -