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

Abstract

Abstract 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 R e 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 R e , 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 ⩽ R e < 230 ), the mode swapping or coexistence stage between modes A and B ( 230 ⩽ R e < 260 ∼ 265 ), the self-adjustment stage of the nondimensional spanwise wavelength from 0.8 to 1 in dominant mode B ( 260 ∼ 265 ⩽ R e < 310 ), and the full development stage of mode B ( R e ⩾ 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 Π − vortex in mode A and the Π + vortex in mode B, in which Π − and Π + vortices are vortices with three vorticity components satisfying the vorticity sign law and shed from the upper and lower shear layers, respectively.