DNS Study on Vortex and Vorticity in Late Boundary Layer Transition (Communications in Computational Physics, 2018)
Vortex and vorticity are two correlated but fundamentally different conceptswhich have been the central issues in fluid mechanics research. Vorticity has rigorousmathematical definition (curl of velocity), but no clear physical meaning. Vortex hasclear physical meaning (rotation) but no rigorous mathematical definition. For a longtime, many people treat them as a same thing. However, based on our high-order directnumerical simulation (DNS), we found that first, "vortex" is not "vorticity tube"or "vortex tube" which is widely defined as a bundle of vorticity lines without anyvorticity line leak. Actually, vortex is an open area for vorticity line penetration. Second,vortex is not necessarily congregation of vorticity lines, but dispersion in many3-dimensional cases. Some textbooks say that vortex cannot end inside the flow fieldbut must end on the solid wall (and/or boundaries). Our DNS observation and manyother numerical results show almost all vortices are ended inside the flow field. Finally,a more theoretical study shows that neither vortex nor vorticity line can attachto the solid wall and they must be detached from the wall.