The fluid flow due to two submerged sinks in a two layer stratified fluid

A boundary integral technique is developed to study the free surface flow of a steady, two‐dimensional, incompressible, irrotational and inviscid fluid flow which is produced by two submerged sinks (or sources) which are of equal strength, placed along a solid horizontal boundary with a stagnation point on the free surface in a two layer stratified fluid in the presence of gravity. A special form of the Riemann‐Hilbert problem, namely the Dirichlet boundary problem, is applied in the derivation of the governing non‐linear boundary integral‐differential equations which are solved for the fluid velocity on the free surface and this involves the use of an interpolative technique and an iterative process. Results have been obtained for the free surface flow for various values of the Froude number and sink locations on the solid horizontal boundary and we have also studied the largest value of the Froude number for which no convergent solutions are possible, namely the critical Froude number. We have found that the free surface profile is dependent on two parameters, namely the Froude number on the free surface and the non‐dimensional distance between the two sinks.