Numerical Study on Collisions of Solitons of Surface Waves in Finite Water Depth

Abstract

Head-on collisions between two solitary waves in the framework of the nonlinear Schrödinger (NLS) equation were investigated using the Fourier spectral method. When solitary waves undergo collision, the peak value of surface elevation (hereafter referred to as ζmax) exhibits fluctuations with increasing relative water depths k0h (where k0 is the wave number and h is the water depth). ζmax is approximately equal to the sum of the peak values of the two solitary waves with smaller wave steepness ε0 (ε0 = k0a0, a0 is the free background amplitude parameter), and it exhibits fluctuations for ε0 > 0.10. Similar results have been observed in the study of head-on collisions for four solitary waves. These results show that the water depth and wave steepness play important roles in the collision of solitary waves, and the effects of the interactions of intense wave groups are important in studies of the mechanisms and manifestations of freak oceanic waves.

Keywords

• solitary waves
• collision
• nonlinear Schrödinger equation
• water waves
• Fourier spectral method