Numerical Study on the Evolution of Peregrine Breathers in Variable Depths

The Peregrine breather (PB), a classical localized solution of the nonlinear Schrödinger equation (NLSE), is widely used to describe the evolution of deep-water rogue waves. However, the influence of variable bathymetry on PB focusing remains insufficiently understood. A two-dimensional RANS–VOF numerical wave tank is therefore established using computational fluid dynamics (CFD) to investigate deterministic PB propagation over variable bathymetry. The model is validated through mesh- and time-step-sensitivity analyses and comparison with the analytical PB solution. Relative water depth, bathymetric interaction length, and bathymetric position are systematically examined. The results reveal for the first time a bathymetry-induced delayed-focusing phenomenon: the PB undergoes local defocusing over elevated topography and refocuses farther downstream after re-entering deeper water. The delay increases as water depth decreases. For k0hshelf > 1.363, increasing the interaction length mainly enhances the focusing delay, while self-focusing recovers in deeper water. In contrast, for k0hshelf < 1.363, an interaction length of approximately two carrier wavelengths disrupts the coherent PB structure and splits it into two wave packets. The onset position of bathymetric forcing has only a minor effect on the final delay. These results clarify how variable bathymetry modulates PB focusing and structural stability and provide a theoretical reference for nearshore extreme-wave risk assessment.