International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 4, Pages 737-754

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

Copyright © 1983 Rathindra Nath Chakrabarti and Birendranath Mandal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.