Linear and Nonlinear Solutions of Interfacial Waves Due to a Doublet
Received:February 20, 2023  Revised:January 06, 2024
Key Words: interfacial waves   doublet   boundary integral equation method   linear solutions  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.52171251; U2106225).
Author NameAffiliation
Di WANG School of Mathematics, Jilin University, Jilin 130012, P. R. China 
Zhen WANG School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China 
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      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.
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