dorsal/arxiv
View SchemaOn the origin of non-Gaussian statistics in hydrodynamic turbulence
| Authors | C. Meneveau, Y. Li |
|---|---|
| Categories | |
| ArXiv ID | physics/0508211 |
| URL | https://arxiv.org/abs/physics/0508211 |
Abstract
Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain-rate with highly non-Gaussian statistics. Quantitatively, intermittency is manifested in highly elongated tails in the probability density functions of the velocity increments between pairs of points. A long-standing open issue has been to predict the origins of intermittency and non-Gaussian statistics from the Navier-Stokes equations. Here we derive, from the Navier-Stokes equations, a simple nonlinear dynamical system for the Lagrangian evolution of longitudinal and transverse velocity increments. From this system we are able to show that the ubiquitous non-Gaussian tails in turbulence have their origin in the inherent self-amplification of longitudinal velocity increments, and cross amplification of the transverse velocity increments.
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"date_created": "2026-03-02T18:01:00.911000Z",
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"abstract": "Turbulent flows are notoriously difficult to describe and understand based on\nfirst principles. One reason is that turbulence contains highly intermittent\nbursts of vorticity and strain-rate with highly non-Gaussian statistics.\nQuantitatively, intermittency is manifested in highly elongated tails in the\nprobability density functions of the velocity increments between pairs of\npoints. A long-standing open issue has been to predict the origins of\nintermittency and non-Gaussian statistics from the Navier-Stokes equations.\nHere we derive, from the Navier-Stokes equations, a simple nonlinear dynamical\nsystem for the Lagrangian evolution of longitudinal and transverse velocity\nincrements. From this system we are able to show that the ubiquitous\nnon-Gaussian tails in turbulence have their origin in the inherent\nself-amplification of longitudinal velocity increments, and cross amplification\nof the transverse velocity increments.",
"arxiv_id": "physics/0508211",
"authors": [
"C. Meneveau",
"Y. Li"
],
"categories": [
"physics.flu-dyn"
],
"title": "On the origin of non-Gaussian statistics in hydrodynamic turbulence",
"url": "https://arxiv.org/abs/physics/0508211"
},
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