DNS in evolution of vorticity and sign relationship in wake transition of a circular cylinder: (pure) mode A

In the present paper, the spatio-temporal evolution of vorticity in the first wake instability, i.e., (pure) mode A, is investigated in order to understand the wake vortex dynamics and sign relationships among vorticity components. Direct numerical simulation (DNS) for the flow past a circular cylinder is performed, typically at a Reynolds number of 200, in the three-dimensional (3-D) wake transition. According to characteristics of time histories of fluid forces, three different stages are identified as the computational transition, the initial stage and fully developed wake. In the second initial stage, the original two-dimensional spanwise vortices become obviously three-dimensional associated with the streamwise or vertical vorticity intensified up to about 0.1. As a matter of fact, these additional vorticities, caused by the intrinsic 3-D instability, are already generated firstly on cylinder surfaces early in the computational transition, indicating that the three-dimensionality appeared early near the cylinder. The evolution of additional components of vorticity with features the same as mode A shows that (pure) mode A can be already formed in the late computational transition. Through careful analysis of the vorticity field on the front surface, in the shear layers and near wake at typical times, two sign laws are obtained. They illustrate intrinsic relationships among three vorticity components, irrelevant to the wavelength or Fourier mode and Reynolds number in (pure) mode A. Most importantly, the origin of streamwise vortices is found and explained by a new physical mechanism based on the theory of vortex-induced vortex. As a result, the whole process of formation and shedding vortices with these vorticities is firstly and completely illustrated. Other characteristics are presented in detail.