International Journal of Mathematics and Mathematical Sciences 
Volume 6 (1983), Issue 4, Pages 737-754
doi:10.1155/S0161171283000630

Singularities in a two-fluid medium

Rathindra Nath Chakrabarti1 and Birendranath Mandal2

 1Narikeldanga High School, 50, Kavi Sukanta Sarani, Calcutta 700085, India
2Department of Applied Mathematics, Calcutta University, 92, Acharya Prafulla Chandra Road, Calcutta 700009, India
Received 30 December 1981; Revised 30 August 1982

Abstract

We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity. The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity. We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered.