Numerical simulations of gravity waves with high-order nonlinearities in two dimensional domain are performed by using pseudo spectral method.
High-order nonlinearities more than third-order excite apparently chaotic evolutions of the Fourier energy in deep-water random waves.
The high-order nonlinearities increase kurtosis, wave height distribution and
in deep-water and decrease these wave statistics in shallow water.
They, moreover, can generate a single extreme high wave with an outstanding crest height in deep-water.
The high-order nonlinearities more than third-order can be regarded as one of the reason for a cause of a freak wave in deep-water.
