In general, Keulegan-Carpenter number is defined by KC = UmT/D, where Um is the maximum velocity of the flow, T is the period of the wave motion, and D is the cylinder diameter. For unidirectional, sinusoidal motion of the fluid past the cylinder, this definition reduces to KC = 2pa/D, where a is the amplitude of the motion. It can be shown that for a small-amplitude wave of wavelength 2p/k,
This formula can be extended to cases where the trajectory of a fluid particle motion is elliptical. In these cases, the amplitude of the wave is multiplied by the orbital parameter W, which is defined as the ratio of the major to the minor axes of the ellipse. From Lighthill (1978), it can be shown that W = cosh[k(d-h0)]/sinh[k(d-h0)].
In these experiments, the general definition of Keulegan-Carpenter number KC = UmT/D was used, where maximum flow velocity Um was measured experimentally (figure A-1). Velocity magnitude was obtained from each PIV image of instantaneous velocity field by calculating mean values of u and v velocity components from a small undisturbed region of the flow field. Um was found as a maximum of calculated velocity magnitudes. For all three depths of submergence (h0 = 20 mm, h0 = 7 mm, and h0 = 0 mm) Um was found to be equal 0.04 m/sec. For the wave period T = 2 sec and diameter of the cylinder D = 0.0127 m, Keulegan-Carpenter number was found to be equal 6.96.