Obliquely interacting breathers in a three-layer fluid

Abstract

In a three-layer system with equal upper and lower thin layers with the same density jump across each interface, fully nonlinear governing equations have revealed that breathers exist under the Boussinesq approximation. Also, it has been demonstrated that breathers may occur in the Baltic Sea. Additionally, in previous studies, it has been shown that the larger the upper- and lower-layer thicknesses, the more the breathers behave like solitons and that phase shifts occur after two breathers interact, with a forward/backward shift of the faster/slower breather, while the properties of the breathers are preserved. Still, the oblique interaction of breathers has yet to be explored. Thus, we aimed to investigate oblique breather interactions in a three-layer system by using fully nonlinear numerical simulations to clarify the characteristics of breathers. The ratio of the thin layer thicknesses to the total depth was 0.25 in this study. Breathers have two significant parameters, p and q, corresponding to the wavelength of a breather and the envelope amplitude. So, we had several configurations to clarify the influence of incident angles and amplitudes on the breather interactions by changing the parameters p and q. Stably progressing breathers, where p and q are 0.025 and 0.006, were examined by changing the incident angles from 10 to 40 degrees to estimate a critical angle. Also, the oblique breather interactions with a larger envelope amplitude were simulated to analyse the amplitude dependence of the critical angle. A Mach stem was found to occur in oblique breather interactions. Also, the critical angle was revealed to decrease as the envelope amplitude decreases. The behaviour of obliquely-interacting breathers provides further evidence that breathers in a three-layer fluid have soliton-like characteristics.