Reconnection of skewed vortices
Journal of Fluid Mechanics
Based on experimental evidence that vortex reconnection commences with the approach of nearly anti-parallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly anti-parallel, they are annihilated on a time-scale that remains O(1) as the kinematic viscosity ν tends to zero. Axial flow can be included, giving
... cluded, giving helical vortex lines in each vortex whose pitch increases exponentially under the action of the ambient strain field. When the vortices are skew to each other, then under this action they are annihilated over a local extent that increases exponentially in the stretching direction, with again clear evidence of reconnection on an O(1) time-scale. The initial writhe helicity associated with the skewed geometry is eliminated during the process of reconnection, and is not compensated by creation of twist helicity. † This ignores the swirl component of velocity Γ/2πr at small distance r from any element of the vortex, which does not contribute to motion of that element.