Recurrent solutions of the Alber equation initialized by Joint North Sea Wave Project spectra

Abstract

Linear instability of two-dimensional wave fields and its concurrent evolution in time is here investigated by means of the Alber equation for narrow-banded random surface waves in deep water subject to inhomogeneous disturbances. The probability of freak waves in the context of these simulations is also discussed. The instability is first studied for the symmetric Lorentz spectrum, and continued for the realistic asymmetric Joint North Sea Wave Project (JONSWAP) spectrum of ocean waves with variable directional spreading and steepness. It is found that instability depends on the directional spreading and parameters α and γ of the JONSWAP spectrum, where α and γ are the energy scale and the ..