Viscous Drag of Bodies Moving near a Free Surface

Abstract

An integral representation is obtained for the velocity and pressure fields produced by the horizontal motion of two-dimensional bodies below (or on) the free surface of a viscous liquid. This allows consideration of viscous and free surface effects to be incorporated in one model for the prediction of forces on the body. The integral representation is used to consider the simple physical example of the motion of a horizontal flat plate. This illustrates the interaction of viscous and free surface effects since the plate experiences skin friction drag plus drag due to the generation of surface waves by the viscous boundary layer.