Intrinsic relationship of vorticity between modes A and B in the wake of a bluff body

The intrinsic physical relationship of vorticity between modes A and B in the three-dimensional wake transition is investigated. Direct numerical simulations for the flow past a square-section cylinder are carried out at Reynolds numbers of 180 and 250, associated with modes A and B, respectively. Based on the analysis of spacial distributions of vorticity in the near wake, characteristics of the vertical vorticity in modes A and B are identified. Moreover, the relationship of three vorticity components with specific signs is summarized into two sign laws, as intrinsic physical relationships between two instability modes. By the theory of vortex-induced vortex, such two sign laws confirm that there are two and only two kinds of vortex-shedding patterns in the near wake, just corresponding to modes A and B. In brief, along the free stream direction, mode A can be described by the parallel shedding vertical vortices with the same sign, while mode B is described by the parallel shedding streamwise vortices with the same sign. Finally, it is found out that the Π-type vortex is a basic kind of vortex structure in both modes A and B. Keywords: Mode A, Mode B, Wake, Bluff body, Sign la