Secondary instabilities of wakes of a circular cylinder using a finite element method

This study investigates secondary instabilities of periodic wakes of a circular cylinder with infinitely long span. It has been known that after the wake undergoes a supercritical Hopf bifurcation (the primary instability) that leads to two-dimensional von Karman vortex street, the secondary instability occurs sequentially, which results in the onset of three-dimensional flow. Williamson (1996) has reviewed that the periodic wakes over a range of moderate Reynolds number from 140 to 300 are characterized by two critical modes, Mode A and Mode B, which are respectively associated with large-scale and fine-scale structures in span. In order to understand a sequence of bifurcation in transitional wake, in this paper, the stability of periodic flow governed by the linearized Navier-Stokes equations is analyzed by using the Floquet stability theory. By employing the finite elemental discretization with a fine mesh, the numerical results for both simulation and stability analysis have high spatio-resolution. The obtained stability results are in good agreement with experimental data and some relevant numerical results. By means of visualizations of thr three-dimensionally critical flow structures, the existence of Mode A and Mode B is verified from the spatial structures in both the two modes.