The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A finite-volum
e approach with a volume of fluid method is applied to study the Peregrine breather dynamics up to the initial stages of wave breaking. The comparison of the numerical results with laboratory experiments to validate the numerical approach shows very good agreement and suggests that the chosen method is an effective tool to study modulation instability and breather dynamics in water waves with high accuracy even up to the onset of wave breaking. The numerical results also indicate some previously unnoticed characteristics of the flow fields below the water surface of breathers, which might be of significance for short-term prediction of rogue waves. Recurrent wave breaking is also observed.
Being considered as a prototype for description of oceanic rogue waves (RWs), the Peregrine breather solution of the nonlinear Schrodinger equation (NLS) has been recently observed and intensely investigated experimentally in particular within the co
ntext of water waves. Here, we report the experimental results showing the evolution of the Peregrine solution in the presence of wind forcing in the direction of wave propagation. The results show the persistence of the breather evolution dynamics even in the presence of strong wind and chaotic wave field generated by it. Furthermore, we have shown that characteristic spectrum of the Peregrine breather persists even at the highest values of the generated wind velocities thus making it a viable characteristic for prediction of rogue waves.
We demonstrate experimentally multi-bound-soliton solutions of the Nonlinear Schrodinger equation (NLS) in the context of surface gravity waves. In particular, the Satsuma-Yajima N-soliton solution with N=2,3,4 is investigated in detail. Such solutio
ns, also known as breathers on zero background, lead to periodic self-focussing in the wave group dynamics, and the consequent generation of a steep localized carrier wave underneath the group envelope. Our experimental results are compared with predictions from the NLS for low steepness initial conditions where wave-breaking does not occur, with very good agreement. We also show the first detailed experimental study of irreversible massive spectral broadening of the water wave spectrum, which we refer to by analogy with optics as the first controlled observation of hydrodynamic supercontinuum a process which is shown to be associated with the fission of the initial multi-soliton bound state into individual fundamental solitons similar to what has been observe in optics.
