On the origin of mode B instability of the wake of a square cylinder

Three-dimensional numerical simulations of flow passing a square cylinder are performed using a spectral element method. Reynolds numbers of 200 and 300, corresponding to mode A and B respectively, are used to study the two- to three-dimensional transition of the wake flow. It is shown that the wake transition occurs in the early-time prior to the onset of the vortex shedding event. For mode A, the spanwise instability grows exponentially downstream of the cylinder with a constant wavelength in the early-time dynamics and continue after the vortex separation. However, in the case of mode B, the exponential amplification reaches a saturation state before the vortex separation occurs. A splitting of the initially obtained wavelength of the spanwise instability occurs and is related to the splitting of spanwise vortical structures which develops at the cores of the separation bubbles prior to the vortex shedding.