| Abstract: |
| The evolution of a unidirectional wave train on varying bathymetry is well documented while the statistics of crossing seas over uneven bottoms remain poorly understood. This work investigates the spatial evolution of skewness and kurtosis for weakly nonlinear random waves propagating over a slowly varying bottom. To model this complex process, we develop a system of coupled nonlinear Schr\"odigner equations that accounts for the interaction between two obliquely propagating wave trains and variation of water depth. We perform comprehensive numerical simulations using split-step Fourier method and initialize the representative wave field using the JONSWAP spectrum. By examining how the incident angle and bathymetry alter wave statistics, we ultimately demonstrate their combined influence on freak wave generation. |
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