Nonlinear Lift Characteristics of Flat Plate at Incidence in Shallow Water

Abstract

A perturbation study is made of the shallow water flow past a rectangular flat plate at incidence, to predict the nonlinear characteristics of the lift acting on it. It is assumed that the flat plate is slender and its draft is nearly equal to the depth of water and the angle of attack is comparatively large. The flow field is divided into three regions for the analysis. In the flow field near the body of the flat plate, Kirchhoff's dead water flow in two-dimensional vortex layers in consideration of the longitudinal flow velocity. The flow far from the body is expressed apparently as the flow past a porous flat plate in a horizontal plane. In the intermediate field between the near and far field a depthwise averaging technique of Euler's equations with apparent stresses is used to determine the flow velocity incoming to the flat plate. The normal force coefficient, which is equal to one for a two dimensional flat plate as zeroth approximation, is simply expressed by using a drag coefficient of dead water flow. The results obtained are compared with experimental results.