Long-living coherent patterns in the fields of irregular waves in deep water

Long-living coherent wave patterns embedded into the irregular wave fields are studied using the data of extensive numerical simulations of the Euler equations in deep water. The distributions of the rogue wave lifetimes according to the numerical simulations of JONSWAP waves with narrow and broad angle spectra are discussed. The observation of a wave group persisting for more than 200 periods in the direct numerical simulation of nonlinear unidirectional irregular water waves is discussed. Through solution of the associated scattering problem for the nonlinear Schrodinger equation, the persisting group is identified as the intense envelope soliton with remarkably stable parameters. Most of extreme waves occur on top of this group, resulting in higher and longer rogue wave events. It is shown that the persisting wave structure survives under the conditions of directional waves with moderate spread of directions. The survivability of coherent wave patterns is expected to further increase when the waves are guided by currents or the topography.

 

The research is supported by the RSF grant No. 19-12-00253; the study of trapped waves is performed for the RFBR grant No. 21-55-15008.