Numerical Study On The Nonlinear Behaviours Of Wave Surface Elevation

Precise simulation and forecast of wave surface elevation is considered to fields such asocean engineering, air-sea interaction, the dynamics of the upper ocean. Wave surface elevationis the fundamental character of ocean waves. Compared to wave generator in the lab and oceanobservations of wave surface elevation, numerical simulation can simulate complex process fastwith cheap expenses.Song（2006） proposed a second-order expression in consideration of finite water deep andhomogeneous background flows. By using the wavenumber spectrum Combi spectrum，the wavesurface elevation was simulated by computing the probability density distribution and featherparameters C、 E、E₁、λ₃、λ₄（C denotes the level of reduced horizontal wave displacement;E andE1separately indicate energy of the linear wave surface elevation and energy of the totalwave surface elevation; Skewness3shows the statistics of the vertical asymmetry;λ₄denotes wave surface elevation distribution kurtosis compared to the standard distribution）. Heanalyzed the effect of second-order nonlinear term on the wave surface elevation statisticsdistribution and the wave surface elevation variability with wind, water depth, inverse wave ageand the homogeneous background flows.The results showed:（1） The second-order nonlinear term made the wave surface elevation distribution deviatefrom the normal distribution satisfied by the linear wave surface elevation. Compared to thenormal distribution, the range of wave surface elevation became larger; the maximum probabilitydensity and the displacement value associated with wave surface elevation both reduced; theprobability produced larger wave surface elevation increased and the wave surface elevationcorresponding to the peaks are greater than the troughs, which displayed remarkable asymmetryof the wave surface probability distribution.（2） The wave surface elevation was impacted by the wind, the water depth, inverse waveage and the homogeneous background flows. Even in deep water, the energy and skewness werestill induced by the second-order nonlinear term, which created the vertical distributionasymmetry on the average horizontal level and increased the wave energy. Consequently, thenonlinear effects cannot be ignored. Enhanced wind, reduced deep and inverse wave age, or theangle <π/2between the homogeneous background flows and wind increased the radio of second-order energy to total energy, the effect of second-order energy, the skewness ofdimensionless wave surface elevation probability density distribution, vice versa. Especially,when the angle equaled to90°，the homogeneous background flows did not impact on the wavesurface elevation probability density distribution.（3） Considering the same direction of the homogeneous background flows and the wind,though the nonlinear effect was enhanced, the average wave surface elevation was lower than theaverage horizontal level. Considering the opposite direction of the flows and the wind, thoughthe nonlinear effect was enhanced, the average wave surface elevation approximated to theaverage horizontal level.We used the experiment （in Zhangzi Island, Dalian） during2009to examine the computersimulation model under large wind, deep water and strong converse background flows. Theresult demonstrated that the model can better simulate the actual in consideration of thebackground flows, compared to the third-order Gram-Charlier series distribution.