Stability Analysis to Predict Vortex Street Characteristics and Forces on Circular Cylinders

Abstract

The characteristics of the wake are predicted accurately by the critical point of the absolute instability supported by the wake profiles immediately behind the cylinder. Measured profiles at Rn = 56 provide Strouhal number St = 0.13 and at Rn = 140,000 St = 0.21 both in good agreement with experiment. It is also shown that at the undercritical Rn = 34 or for a symmetric array of vortices the instability is of the convective type, decaying behind the cylinder once the excitation is removed. Finally, it is shown that a model of the wake, based on the results of the instability analysis, is sufficient to obtain good estimates of the steady and unsteady forces on the cylinder. Closed-form expressions for the forces are obtained within this approximation.