Numerical study of nonlinear Peregrine breather under finite water depth

Though the focusing method can effectively generate waves which satisfy the definition of rogue waves at a specific position and moment, however, being inherently not nonlinear, the focusing model is still a controversial rogue wave generation method. Recently, nonlinear models are becoming more popular for rogue wave generation in physical and numerical tanks. In this paper, a weakly nonlinear model known as the Peregrine breather solution of the cubic Schrödinger equation is studied under finite water depth. In contrast with the focusing model, nonlinearity is considered throughout the simulation process, i.e., from the wave model to the generated waves. The numerical results are validated against theoretical solutions as well as experimental measurements. To further investigate their temporal-frequency characteristics, a wavelet analysis is performed on the generated Peregrine breather, and the concepts of life time and traveling distance are studied. The influence of higher order nonlinearity, i.e., the 2nd-order Stokes component of the perturbed expansion under finite water depth, is taken into account. We also discuss the influence of 2nd-order term on the life time, travel distance, and energy distribution.