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<qmin≤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.
|Original language||English (US)|
|Number of pages||13|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|State||Published - Oct 1999|
All Science Journal Classification (ASJC) codes
- Applied Mathematics