dorsal/arxiv
View SchemaTurbulent Cascade of Circulations
| Authors | Gregory L. Eyink |
|---|---|
| Categories | |
| ArXiv ID | physics/0605014 |
| URL | https://arxiv.org/abs/physics/0605014 |
| DOI | 10.1016/j.crhy.2006.01.008 |
Abstract
The circulation around any closed loop is a Lagrangian invariant for classical, smooth solutions of the incompressible Euler equations in any number of space dimensions. However, singular solutions relevant to turbulent flows need not preserve the classical integrals of motion. Here we generalize the Kelvin theorem on conservation of circulations to distributional solutions of Euler and give necessary conditions for the anomalous dissipation of circulations. We discuss the important role of Kelvin's theorem in turbulent vortex-stretching dynamics and conjecture a version of the theorem which may apply to suitable singular solutions.
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"abstract": "The circulation around any closed loop is a Lagrangian invariant for\nclassical, smooth solutions of the incompressible Euler equations in any number\nof space dimensions. However, singular solutions relevant to turbulent flows\nneed not preserve the classical integrals of motion. Here we generalize the\nKelvin theorem on conservation of circulations to distributional solutions of\nEuler and give necessary conditions for the anomalous dissipation of\ncirculations. We discuss the important role of Kelvin\u0027s theorem in turbulent\nvortex-stretching dynamics and conjecture a version of the theorem which may\napply to suitable singular solutions.",
"arxiv_id": "physics/0605014",
"authors": [
"Gregory L. Eyink"
],
"categories": [
"physics.flu-dyn",
"physics.ao-ph"
],
"doi": "10.1016/j.crhy.2006.01.008",
"title": "Turbulent Cascade of Circulations",
"url": "https://arxiv.org/abs/physics/0605014"
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