Asymmetrical interaction of solitary waves in idealized converging water bodies

Solitary waves are commonly used to model long waves, such as tsunamis. Limited research is available for such waves propagating in converging water bodies, such as fjords, bays, and estuaries, where reflection and large amplified waves can be observed. Therefore, an extended analytical solution is presented to calculate the non-dimensional asymptotic amplified wave amplitude Aw and its trajectory for the oblique interaction of two distinct weakly non-linear solitary waves based on line-soliton solutions of the Kadomtsev–Petviashvili equation. Furthermore, an analytical model is developed for wave propagation in a converging geometry featuring Mach reflection. An oblique angle ψ̂ of Mach stem and a general stem angle φ are defined, along with their explicit calculation formulas. The Simulating WAves till SHore model based on the non-hydrostatic, non-linear shallow water equations, is used to validate the solutions and the analytical model numerically. The simulation results for Aw and ψ̂ show asymptotic behavior and converge toward the prediction of the extended solutions. At an average oblique angle of 17° between two solitary waves, the discrepancy between the numerical and analytical results for Aw is up to −9.0% for the first-order and +8.3% for the second-order solutions, respectively. For the most asymmetrical converging geometry examined, the simulated result of φ=14.2° remains 92.0% of the theoretical value. These findings indicate that the proposed solutions can readily and accurately predict the angles and amplitudes of amplified waves resulting from the interaction of weakly non-linear solitary waves in extensive converging water bodies.