Numerical study of Rogue waves as nonlinear Schrödinger breather solutions under finite water depth

• Peregrine breather of cubic Schrödinger equation is applied to numerical tanks.
• Nonlinear rogue waves are generated without introducing any linear effect.
• Meaningful results are found by using the wavelet analysis.
• Realistic rogue waves in the ocean are generated using Peregrine breather.

Following the existing experimental investigations, in this paper, we perform a series of simulations on rogue waves based on a breather solution of the cubic Schrödinger equation, in a numerical wave tank coded in Visual Basic language. The numerical wave tank solves 2-D Navier–Stokes equations and constructs free surfaces with a volume of fluid method. The simulated results are compared against theoretical solutions, and further analyzed by the Fast Fourier Transformation in the frequency domain. Besides, the wavelet analysis is employed, to obtain the temporal-frequency spectrum of the simulated rogue waves. Finally a realistic rogue wave measured in the Sea of Japan is simulated to validate breather solutions under realistic sea states.