Spanwise phase transition between pure modes A and B in a circular cylinder's wake. Part II: spatiotemporal evolution of vorticity

Through direct numerical simulation, the transition from pure mode A to mode B in the near wake of a circular cylinder is studied without consideration of vortex dislocations. The Reynolds number Re is calculated from 100 to 330 with a computational spanwise length of 4 diameters. In the present section, the spatiotemporal evolution of the vorticity and its sign are analyzed. The results show that mode B, as a kind of weak disturbed vorticity with opposite signs, actually appears partially on the rear surface of the cylinder and in the shear layers once Re exceeds 193. With increasing Re, the vortex-shedding patterns in the near wake undergo the initial generation stage of mode B coupling with the fully developed pure mode A (193 <= Re < 230), the mode swapping or coexistence stage between modes A and B (230 <= Re < 260 similar to 265), the self adjustment stage of the nondimensional spanwise wavelength from 0.8 to 1 in dominant mode B (260 similar to 265 <= Re < 310), and the full development stage of mode B (Re >= 310). In particular, the spanwise phase transition initially occurs at a certain spanwise position in the initial generation stage where a part of mode A and a part of mode B with specific vorticity signs appear, e.g. the Pi(-) vortex in mode A and the Pi(+) vortex in mode B, in which Pi- and Pi+ vortices are vortices with three vorticity components satisfying the vorticity sign law and shed from the upper and lower shear layers, respectively.