Study on vorticity structures in late flow transition

A focus is presented on the investigation of vorticity generation and development and the vorticity structures inside/outside of a vortex. A vortex cannot be directly represented only by the vorticity, but is a region where the vorticity overtakes deformation. Except for those vorticity lines which come from and end at side boundaries, another type, self-closed vorticity lines named vorticity rings, is numerously generated inside the domain during flow transition. Vorticity and vortex are two different but closely related concepts, and both new vorticity and new vortices are generated during flow transition. According to our direct numerical simulation result, the generation and growth of the vorticity rings are produced by the buildup of the vortex; on the other hand, the vortex buildup is a consequence of the lengthening (stretching, tilting, and twisting) of the vorticity lines. According to the vorticity flux conservation law, a vorticity line cannot be interrupted, started, or ended inside the flow field; the newly generated vorticity has only one form which is a vorticity ring. In addition, for a single hairpin vortex or a ring-like vortex, it may consist of several types of vorticity lines: some could come from the side boundaries and some could be full of vorticity rings or part of vorticity rings.