A Transition of the Intensity of Swirling of Vorticity Lines with Coalescence of Vortical Regions in a Homogeneous Isotropic Turbulence*

The present study analyses the transition of coalescence of vortical regions in the core regions of vortices and traces the topology of bundles of vorticity lines using the local axis geometry. A coalescing phenomenon of vortices has been observed in a homogeneous isotropic turbulence, where the velocity field composes a large swirling motion in the swirl plane in the coalesced vortex. However, swirlity that specifies the swirling of the flow in terms of the local topology shows that this swirling motion is composed of two vortices in the same swirl plane. In addition, the vorticity lines swirl in the plane, and  the intensity of swirling increases at the coalescence part. This result suggests that the swirling feature of vorticity vectors may become intense due to the coalescing phenomenon. The vorticity vectors show a swirling feature when the non-diagonal components of the vorticity gradient tensor in the plane have the opposite signs in the swirl plane. The distributions of the components in the coalesced vortex show the complex feature in comparison with the non-coalesced vortex. It shows that the coalesced vortex is associated with a complicated phenomenon in terms of the topology of the vorticity vectors.