New solutions for periodic interfacial gravity waves

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673-708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

Automated summary

The study considers two-dimensional periodic interfacial gravity waves between two homogeneous fluids of finite depth. Highly accurate solutions are obtained using a boundary-integral-equation method coupled with Fourier expansions. The numerical results show excellent agreement with those obtained using a different scheme, exploring the global bifurcation mechanism and identifying three types of limiting wave profiles.