BASIC SINGULARITIES IN THE THEORY OF INTERNAL WAVES
M. A. Gorgui, S. E. Kassem · The Quarterly Journal of Mechanics and Applied Mathematics · 1978
The study of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing these singularities are obtained, neglecting effects of surface tension at the surface of separation. Line and point singularities are considered for the cases when the lower fluid is of infinite and of finite constant depth, the upper being of infinite height. The method used is an extension of that which had been used to obtain such potentials for one-fluid problems. Velocity potentials are also obtained when the singularities are at the surface of separation.