### Abstract

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form L approximately integral k(alpha)/vk/2dk in 3D Fourier representation, where alpha is a constant, 0<alpha<1. Unlike the case alpha=0 (the usual Eulerian hydrodynamics), a finite value of alpha results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of antiparallel vortex filaments and an analog of the Crow instability is found at small wave numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like (t*-t)(1/(2-alpha)), where t* is the singularity time.

Original language | English |
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Journal | Physical Review E |

Volume | 63 |

Issue number | 5 |

Pages (from-to) | 056306.1 - 056306.9 |

ISSN | 2470-0045 |

DOIs | |

Publication status | Published - 2001 |

## Cite this

Ruban, V. P., Podolsky, D. I., & Juul Rasmussen, J. (2001). Finite time singularities in a class of hydrodynamic models.

*Physical Review E*,*63*(5), 056306.1 - 056306.9. https://doi.org/10.1103/PhysRevE.63.056306