The Stuart–Landau model applied to wake transition revisited

Following previous experimental and computational studies, this article further investigates the applicability of the Stuart– Landau equation to describe the Hopf bifurcation occurring for flow past a circular cylinder. 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. The variation with downstream distance is quantified. 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. It is shown that if the amplitude variable is taken as the lift coefficient of the cylinder (a global variable) then the same Landau constant is measured at saturation and the zero amplitude Landau constant corresponds to that for the transverse velocity at the back of the cylinder. These findings are used to interpret the wake behaviour of a transversely oscillating circular at subcritical Reynolds numbers.  2003 Elsevier SAS. All rights reserved.