Wake formation around islands in oscillatory laminar shallow-water flows. Part 1. Experimental investigation

Abstract

An experimental investigation of oscillatory shallow-water flow around islands has been undertaken to determine the dependence of wake formation on Keulegan–Carpenter number, KC = UoT/D, and stability parameter, S = cfD/h, where Uo is amplitude of velocity oscillation, T is oscillation period, D is a representative island diameter, cf is friction coefficient and h is water depth. Two geometries are investigated: a vertical cylinder and a conical island with a small side slope of 8°. Existing experimental results for current flow around the same geometries have shown the influence of the stability parameter. Predominantly laminar flows are investigated and the flows are subcritical.Four modes of wake formation have been identified for both geometries: one with symmetric attached counter-rotating vortices only forming in each half-cycle, one with vortex pairs forming symmetrically in addition in each half-cycle, one with vortex pairs forming with some asymmetry and one with complex vortex shedding. The last results from one of the attached vortices crossing to the opposite side of the body during flow reversal; in the other cases the attached vortices are convected back on the same sides. For convenience these formations are called: symmetric without pairing, symmetric with pairing, sinuous with pairing and vortex shedding. They are shown on KC/S planes for both geometries. Numerical modelling of the flows for the conical island, based on the three-dimensional shallow-water equations with the hydrostatic pressure assumption, is undertaken in Part 2 (Stansby & Lloyd 2001).