In the present numerical study we report growth of four different unsteady modes of Hopf bifurcation in the wake of a square cylinder. During the transient process of wake evolution there occurred frequent switching between the bifurcation modes, and along the corelines of the shedded vortices the instantaneous flow thereby evolved through single/multiple modes of Hopf bifurcations.
In recent years, there has been growing interest of exploring different possible routes leading to flow transition in bluff body wakes, and establishing links between various modes of vortex shedding and the growth of associated spatio-temporal instability mechanisms. In this regard, flow around a square cylinder may be considered as an ideal prototype both in terms of simplicity of the physical configuration and relevance of the flow complexity to a wider class of wake evolution. Important to mention here that the major source of instability in bluffbody/jet wake is often thought to be the Hopf bifurcations (as predicted from Stuart-Landau/Ginzburg-Landau equations). However, till today there apparently exists no solid physical evidence demonstrating the fact in a space-time coordinate system, particularly based on Navier- Stokes solutions, and existing literature is very much lacking an in depth understanding of the actual governing flow physics. While a 3D bifurcation phenomenon is difficult to predict experimentally, much of the important past measurements (Williamson,1988; Williamson, 1996; Eisenlohr and Eckelmann, 1989) on bluff body wakes remained focused on accurately estimating the values of the critical Reynolds numbers responsible for wake transitions that correspond to different vortex shedding modes; and additional physical complexities of such flows, as contributed by spanwise end contaminations and their relative measures of elimination (Hammache and Gharib, 1989), often diverted attention away from what could be obtained with the so called clean boundary condition.
