Shallow-Water Flow around Model Conical Islands of Small Side Slope. I: Surface Piercing

Abstract

A series of experiments has been conducted to investigate recirculating shallow-water flow in the wakes of conical model islands with gently sloping sides. Four islands have been used with side slopes ranging from 33.1 to 8.0°. For all tests reported here the water depth was less than the island height; the islands are said to be surface piercing. Measurements of flow velocity have been made in the laboratory using a digital particle tracking velocimetry (PTV) system. This produces instantaneous, whole-field velocity vector maps of the wake flows. A “wake stability parameter,”S has been used to classify the island wakes into “vortex shedding” or “unsteady bubble” types. The stability parameter is a measure of the stabilizing effect of bed friction relative to the destabilizing influence of transverse shear. For small values of S (S (0.35–0.40). These values are similar to those found by other researchers for the shallow wakes of vertically sided circular cylinders. The influence of the island side slope angle on the wakes is discussed. Depth-averaged and three-dimensional (3D) numerical shallow-water flow models with the usual hydrostatic pressure assumption have been used to simulate the experimental flows. The models are based on a fully coupled semi-implicit Lagrangian numerical method. For cases where vortex shedding occurred, the 3D model was found to predict a more 3D far wake than was observed. The two-dimensional (2D) model produced good overall agreement with experimental results. For very shallow depths with the wake stabilized by bed friction, the 3D model demonstrated closer agreement to the measured results than the 2D model.