### Abstract

A sufficient condition is obtained for the development of a finite-time singularity in a highly symmetric Euler flow, first proposed by Kida [J. Phys. Soc. Jpn. 54, 2132 (1995)] and recently simulated by Boratav and Pelz [Phys. Fluids 6, 2757 (1994)]. It is shown that if the second-order spatial derivative of the pressure ([Formula Presented]) is positive following a Lagrangian element (on the x axis), then a finite-time singularity must occur. Under some assumptions, this Lagrangian sufficient condition can be reduced to an Eulerian sufficient condition which requires that the fourth-order spatial derivative of the pressure ([Formula Presented]) at the origin be positive for all times leading up to the singularity. Analytical as well as direct numerical evaluation over a large ensemble of initial conditions demonstrate that for fixed total energy, [Formula Presented] is predominantly positive with the average value growing with the numbers of modes.

Original language | English (US) |
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Pages (from-to) | 1530-1534 |

Number of pages | 5 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 54 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1996 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*54*(2), 1530-1534. https://doi.org/10.1103/PhysRevE.54.1530