The wave resistance of a two-dimensional body moving forward in a two-layer fluid

A two-dimensional body moves forward with constant velocity in an inviscid, incompressible fluid under gravity. The fluid consists of two layers having different densities, and the body is totally submerged in one of them. The resulting fluid motion is assumed to be steady state in a coordinate system attached to the body. The boundary-value problem for the velocity potential is considered in the framework of linearized water-wave theory. The asymptotics of the solution at infinity is obtained with the help of an integral representation, based on the explicitly known Green function. The theorem of unique solvability is formulated, and the method applied to prove it is briefly explained (the detailed proof is given in another work). An explicit formula for the wave resistance is derived and discussed. A numerical example for the wave resistance serves to illustrate the so-called ''dead-water'' phenomenon.