A Re-examination of the Stuart-Landau Model Applied to Cylinder Wake Transition

Following previous experimental and computational studies, we further investigate the applicability of the Stuart-Landau equation to describe the Hopf bifurcation occurring for flow past a circular cylinder. In contrast to previous findings, it is shown that when the amplitude variable is taken as the transverse velocity component at a point in the wake, the so-called Landau constant varies considerably with position and importantly is generally far from constant during the saturation phase of wake development. However, it is found that the Landau constant at saturation is indeed a position-independent constant and this value is close to that generally measured previously both experimentally and numerically.