TY - JOUR

T1 - Maximal energy isolated vortices in a uniform shear flow

AU - Yong-Hui, Wu

AU - Mu, Mu

N1 - Funding Information:
The author would like to thank G.R. Burton for his useful suggestion. This work is supported by the Natural Science Foundation of China (No. 49455007 and 49775262).

PY - 1999/10

Y1 - 1999/10

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.

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

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

M3 - Article

AN - SCOPUS:0033212457

SN - 0362-546X

VL - 38

SP - 123

EP - 135

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 1

ER -