Strouhal numbers associated with the drag crisis

The supercritical Strouhal and critical Reynolds numbers associated with the drag crisis of circular cylinders in cross-flow are known to be dependent on surface roughness and turbulence levels. To better understand the role of free-stream turbulence, we consider the traditional model of oscillating lift forcing together with a randomly fluctuating disturbance associated with fluid turbulence. To the extent that these two components are additive, statistically independent, and Gaussian, we are able to derive a closed-form expression describing the relationship between the effective shedding rate and free-stream turbulence. A semi-empirical model of the critical Reynolds number accounting for fluid turbulence is also presented.