Two-dimensional problem of a uniform flow of a two-layer fluid of finite depth past a circular cylinder

The linear steady problem of an irrotational uniform flow past a horizontal circular cylinder located in the upper or in the lower layer of a two-layer fluid is solved by the multipole-expansion method. The flow is perpendicular to the axis of the cylinder. The fluid is assumed to be inviscid and incompressible, and the flow in each layer is assumed to be potential. The upper layer can be bounded by a free surface or a solid lid, and the lower layer by a rigid horizontal bottom.