Linear and Nonlinear Solutions of Interfacial Waves Due to a Doublet

Steady two-dimensional potential flows of two-layer fluids with a submerged doublet in the lower layer are considered. Both linear analytical solutions and fully nonlinear solutions based on boundary integral equation methods are obtained. Nonlinearity strongly influences the downstream wave height and leads to a slight phase difference. When the Froude number is small, wave height fast gets its maximum as the Froude number increases. While wave-less solutions may be obtained if the Froude number is very large. Afterward, the interfacial waves due to one point vortex or a vortex pair are compared with those due to a doublet. It is found that the nonlinear wave profiles due to a doublet are quite close to those due to a vertical vortex pair if the distance between the vortex pair is set appropriately.