Simulating the evolution of focused waves by a two-layer Boussinesq-type model

Accurate simulation of the evolution of freak waves by the wave phase focusing method requires accurate linear and nonlinear properties, especially in deep-water conditions. In this paper, we analyze the ability to simulate deep-water focused waves of a two-layer Boussinesq-type (BT) model, which has been shown to have excellent linear and nonlinear performance. To further improve the numerical accuracy and stability, the internal wave-generated method is introduced into the two-layer Boussinesq-type model. Firstly, the sensitivity of the numerical results to the grid resolution is analyzed to verify the convergence of the model; secondly, the focused wave propagating in two opposite directions is simulated to prove the symmetry of the numerical results and the feasibility of the internal wave-generated method; thirdly, the limiting focused wave condition is simulated to compare and analyze the wave surface and the horizontal velocity of the profile at the focusing position, which is in good agreement with the measured values. Meanwhile the simulation of focused waves in very deep waters agrees well with the measured values, which further demonstrates the capability of the two-layer BT model in simulating focused waves in deep waters.