Maximal energy isolated vortices in a uniform shear flow

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 S₂, while the more narrow it is along the x₂ direction, the greater is S₁.