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
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.