### Abstract

The existence of the isolated vortex on every isovortical surface under the condition that the vorticity anomaly everywhere has the same sign as the external shear flow is obtained. Moveover, the isolated vortex attains the maximal energy on every isovortical surface and therefore is formally stable. The condition that the vorticity anomaly has a positive lower bound, 0<q_{min}≤q in the case of S>0, which is a very strong restriction to the vorticity anomaly is removed. It is easy to see that the more concentrated upon the center, the greater is S_{2}, while the more narrow it is along the x_{2} direction, the greater is S_{1}.

Original language | English (US) |
---|---|

Pages (from-to) | 123-135 |

Number of pages | 13 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 38 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1999 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Analysis, Theory, Methods and Applications*,

*38*(1), 123-135. https://doi.org/10.1016/S0362-546X(99)00102-9

}

*Nonlinear Analysis, Theory, Methods and Applications*, vol. 38, no. 1, pp. 123-135. https://doi.org/10.1016/S0362-546X(99)00102-9

**Maximal energy isolated vortices in a uniform shear flow.** / Weng, Yonghui; Mu, Mu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Maximal energy isolated vortices in a uniform shear flow

AU - Weng, Yonghui

AU - Mu, Mu

PY - 1999/1/1

Y1 - 1999/1/1

N2 - The existence of the isolated vortex on every isovortical surface under the condition that the vorticity anomaly everywhere has the same sign as the external shear flow is obtained. Moveover, the isolated vortex attains the maximal energy on every isovortical surface and therefore is formally stable. The condition that the vorticity anomaly has a positive lower bound, 0min≤q in the case of S>0, which is a very strong restriction to the vorticity anomaly is removed. It is easy to see that the more concentrated upon the center, the greater is S2, while the more narrow it is along the x2 direction, the greater is S1.

AB - The existence of the isolated vortex on every isovortical surface under the condition that the vorticity anomaly everywhere has the same sign as the external shear flow is obtained. Moveover, the isolated vortex attains the maximal energy on every isovortical surface and therefore is formally stable. The condition that the vorticity anomaly has a positive lower bound, 0min≤q in the case of S>0, which is a very strong restriction to the vorticity anomaly is removed. It is easy to see that the more concentrated upon the center, the greater is S2, while the more narrow it is along the x2 direction, the greater is S1.

UR - http://www.scopus.com/inward/record.url?scp=0033212457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033212457&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(99)00102-9

DO - 10.1016/S0362-546X(99)00102-9

M3 - Article

AN - SCOPUS:0033212457

VL - 38

SP - 123

EP - 135

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 1

ER -