Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz equation
Consider a two-fluid medium, both fluids being inviscid and incompressible. The mean surface of separation is taken as the x-z plane. A line source is present in either fluid such that the singular point is located at (0,\(\eta)\) or (0,-\(\eta)\) \((\eta >0)\). The strength of the source varies sinusoidally with time and z. The motion is assumed irrotational and of small amplitude. The problem is decomposed into two boundary value problems. Using the solution of the Laplacians as the intermediate stage, the potential is obtained. Cases of wave sources and finite depth of the lower fluid are considered as also the requirement of an out-going wave solution. The limiting situations of a static potential in a one fluid medium and of a time harmonic line source in a two fluid medium are indicated.
scientific article; zbMATH DE number 3980714