In deep-water, quasi-resonant four-wave interaction gives rise to the occurrence probability of extreme wave height, which leads to freak wave as a natural disaster. As water wave enters shallow water, four-wave interaction becomes weak and wave shoaling makes this effect become complicated. This study conducts a Monte Carlo simulation in modified Nonlinear Schrödinger equation considering bottom topography change, and gives spatial evolution of high-order nonlinearity in wave train from statistical moment. The result indicates, slope angle plays an important role in a shallow water depth, and steep slope brings about a significant enhancement of extreme event in distribution of maximum wave height and surface elevation.

在深水中，准谐振四波相互作用会引起极端波高的发生概率，从而导致畸形波成为自然灾害。当水波进入浅水区时，四波相互作用变弱，波的浅滩作用使该作用变得复杂。这项研究在考虑底部地形变化的情况下，在修改后的非线性Schrödinger方程中进行了蒙特卡洛模拟，并从统计时刻给出了波列中高阶非线性的空间演化。结果表明，倾斜角在浅水深度中起着重要作用，而陡峭的坡度在最大波高和地表高程的分布方面极大地增强了极端事件。