A boundary-Integral Equation for Two-Dimensional Oscillatory Stokes Flow Past an Arbitrary Body

The fundamental singular velocity and pressure fields generated by the presence of an isolated line force acting at a point in a two-dimensional unbounded viscous incompressible medium executing oscillatory motions are used to formulate an integral equation which governs the flow past an arbitrarily shaped body. The Fredholm integral equation of the first kind is then solved by means of a boundary-element method, for the translational oscillatory flow past circular, elliptic and orthogonally intersecting cylinders. The asymptotic behaviour of the force on the cylinder for large values of the frequency parameter is obtained.