dorsal/arxiv
View SchemaBreaking of vortex lines - a new mechanism of collapse in hydrodynamics
| Authors | E. A. Kuznetsov, V. P. Ruban |
|---|---|
| Categories | |
| ArXiv ID | physics/0009007 |
| URL | https://arxiv.org/abs/physics/0009007 |
Abstract
A new mechanism of the collapse in hydrodynamics is suggested, due to breaking of continuously distributed vortex lines. Collapse results in formation of the point singularities of the vorticity field $|{\bf\Omega}|$. At the collapse point, the value of the vorticity blows up as $(t_0-t)^{-1}$ where $t_0$ is a collapse time. The spatial structure of the collapsing distribution approaches a pancake form: contraction occurs by the law $l_1\sim(t_0-t)^{3/2}$ along the "soft" direction, the characteristic scales vanish like $l_2\sim(t_0-t)^{1/2}$ along two other ("hard") directions. This scenario of the collapse is shown to take place in the integrable three-dimensional hydrodynamics with the Hamiltonian ${\cal H}=\int|{\bf\Omega}|d{\bf r}$. Most numerical studies of collapse in the Euler equation are in a good agreement with the proposed theory.
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"abstract": "A new mechanism of the collapse in hydrodynamics is suggested, due to\nbreaking of continuously distributed vortex lines. Collapse results in\nformation of the point singularities of the vorticity field $|{\\bf\\Omega}|$. At\nthe collapse point, the value of the vorticity blows up as $(t_0-t)^{-1}$ where\n$t_0$ is a collapse time. The spatial structure of the collapsing distribution\napproaches a pancake form: contraction occurs by the law $l_1\\sim(t_0-t)^{3/2}$\nalong the \"soft\" direction, the characteristic scales vanish like\n$l_2\\sim(t_0-t)^{1/2}$ along two other (\"hard\") directions. This scenario of\nthe collapse is shown to take place in the integrable three-dimensional\nhydrodynamics with the Hamiltonian ${\\cal H}=\\int|{\\bf\\Omega}|d{\\bf r}$. Most\nnumerical studies of collapse in the Euler equation are in a good agreement\nwith the proposed theory.",
"arxiv_id": "physics/0009007",
"authors": [
"E. A. Kuznetsov",
"V. P. Ruban"
],
"categories": [
"physics.flu-dyn"
],
"title": "Breaking of vortex lines - a new mechanism of collapse in hydrodynamics",
"url": "https://arxiv.org/abs/physics/0009007"
},
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