The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves

Abstract

This study concerns the flow around the base of a vertical, wall-mounted cylinder - a pile - exposed to waves. The study comprises (i) flow visualization of horseshoe-vortex flow in front of and the lee-wake-vortex flow behind the pile and (ii) bed shear stress measurements around the pile conducted in a wave flume, plus supplementary bed shear stress measurements carried out in an oscillatory-flow water tunnel. The Reynolds number range of the flume experiments is Re D = (2-9) x 10 3 and that of the tunnel experiments is Re D = 10 3 —5 x 10 4 , in which Re D is based on the pile size. Steadycurrent tests were also carried out for reference. The horseshoe-vortex flow (like leewake-vortex flow) is governed primarily by the Keulegan-Carpenter number, KC. The range of KC was from 0 to about 25 in the flume experiments, and from 4 to 120 in the tunnel experiments. The experiments were conducted mainly with circular piles. The results indicate that no horseshoe vortex exists for KC < 6. The size and lifespan of the horseshoe vortex increase with KC. The influence of the cross-sectional shape of the pile on the horseshoe vortex was investigated. The results show that a square pile with 90° orientation produces the largest horseshoe vortex while that with 45° orientation produces the smallest one, the circular-pile result being between the two. The influence of a superimposed current on the horseshoe vortex was also investigated. The range of the current-to-wave-induced-velocity ratio, U c /U m , was from 0 to about 0.8. The overall effect of the superimposed current is to increase the size and lifespan of the horseshoe vortex. This effect increases with increasing U c /U m . Regarding the near-bed lee-wake flow, the flow regimes observed for the two-dimensional free-cylinder case exist for the present case, too, but with one exception: in the present case, no transverse vortex street was observed in the so-called single-pair regime. The results show that the bed shear stress beneath the horseshoe vortex and in the lee-wake area is heavily influenced by KC. The amplification of the bed shear stress with respect to its undisturbed value is maximum ( O (4)) at the side edges of the pile, in contrast to what occurs in steady currents where the maximum occurs at an angle of about 45° from the upstream edge of the pile with an amplification of O (10).