Numerical simulation of directional JONSWAP sea waves taking into account four- and five-wave nonlinear resonances

We perform the direct numerical simulation of surface gravity waves in the deep sea with the initial conditions specified by waves with a given JONSWAP spectrum and the directional spreading according to the cos² distribution. The High Order Spectral Method employed for the simulation, allows to control the order of nonlinearity through the parameter of the scheme, M. In particular, the value M = 1 corresponds to the linear solution, M = 3 – to the account of the cubic nonlinearity due to the four-wave nonlinear interactions. Most of the direct numerical simulations of the HOSM available in the literature, are performed with the parameter M = 3, which is sufficient to take into account the modulational instability. In this work we examine the role of even higher order nonlinear effects due to 5-wave interactions. To this end, a series of comparative numerical simulations have been performed with M = 3 and M = 4. The obtained wave data are examined with respect to the probability distribution functions for the wave heights, and the typical rogue wave shapes. So far, no new dynamical effects between waves associated with the high-order nonlinearity is found. The high-order nonlinearity seems to affect the dynamics of very steep waves leading to the generation of even slightly higher waves. The main part of the wave height probability distribution function remains unchanged.

 

The research is supported by the RFBR grants Nos. 20-05-00162 and 21-55-15008.

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