Experimental and numerical study on freak wave using the Peregrine breather

Abstract

The evolution of the Peregrine breather (PB) in a wave tank is experimentally studied under water depths k0h (where k0 represents the wave number and h the water depth) ranging from 4.35 to 5.24. Additionally, the initial wave steepness, ε0=k0a0 (with a0 being the background wave amplitude), was varied within the range of 0.077 to 0.116. Comparative analysis between the experimental observations and the numerical simulations, conducted using the high-order nonlinear Schrödinger equation (HNLSE), revealed that the HNLSE proficiently captures intricate details of wave field evolution, including a pronounced left–right asymmetry in surface elevations. The numerical outcomes demonstrated a high degree of consistency with the experimental data. Furthermore, numerical methodologies were employed to examine the fluctuation of wave height relative to water depth. The results of these simulations suggested that as water depth transitions from shallow to deeper conditions, the wave height amplification factor diminishes, eventually stabilizing. This implies that under shallower water conditions, there is a propensity for larger wave generation.