本文以數值模擬方法研究非線性深水波列傳播過程之演變。基於弱非線性與波列緩慢調變之假設，利用攝動參數法及虛擬微分運算子轉換推導得到移動座標系統下，時間演變之四階非線性薛丁格方程式(nonlinear Schrödinger equation, NLS)。以虛擬頻譜轉換法(pseudospectral transform)配合兩時間步階處理時間微分項，完成數值模式之建構。數值模擬的結果並與物理模型實驗資料作比較。

　　對於非碎波試次，於兩波(雙頻波)試次即使波列傳播相當的距離，水位振幅及全頻譜圖仍有很好的相似性。於三波(一主頻及一組微小副頻)之未碎波試次，在低副頻達最大成長率(調變達最強)前於水位振幅及全頻譜圖皆有很好的相似性，其後數值模擬能量往高頻傳遞機制，較實際機制不明顯以致相關預測不是很精準，但趨勢大致相同。

　　而對於碎波試次，同樣在低副頻達最大成長率前水位振幅及全頻譜圖皆有很好的相似性，但其後因數值模式未考慮碎波導致能量消散及改變能量傳輸之機制，致使模式模擬之演變趨勢與實際演變趨勢不符合。因此，本文進一步於模式中加入往昔文獻所提出之模擬碎波效應函式進行模擬，並以三波碎波試次加以驗證，結果顯示現有碎波函式對於碎波後的趨勢大致符合，然對於能量傳輸定量描述能力仍有不及且對於多次碎波後的成長趨勢，有待未來更進一步研究。

　　Numerical and physical experiments on nonlinear wave train were conducted in deep water. The evolution of wave train and spectra was investigated in this paper. Based on the assumptions of slowly varying wave train and weak nonlinearity, the evolution of wave train can be described by the nonlinear Schrödinger equation (NLS). Trulsen and Stansberg (2001) derived the spatial domain model of fourth order nonlinear Schrödinger equation. Following the transformation proposed by Lo and Mei (1985), a normalized spatial domain model of fourth order nonlinear Schrödinger equation in moving coordinate system can be derived. The numerical scheme combined with the pseudo-spectra method and split step method for time integration was used to solve the evolution equation, and structured the numerical model. The result of numerical simulation also compared with the experimental data with physical model.

　　For non-breaking bichromatic wave case, the periodic modulation and demodulation of wave train were observed in numerical and experimental results. Both the surface elevation and the spectra are matched well with the experimental data, even the wave group propagated certain far distance. For non-breaking three wave cases, constructed by one foundation frequency with a set of two the same small amplitude of sideband frequency, both the amplitude of elevation and the spectra were matched well with the experimental data before the low sideband reached the maximum growth rate. After maximum growth rate, the amplitude of elevation and the spectra didn’t match well with experimental data which was reasoned to the energy spread out the high wave number modes of numerical simulation was less apparent than the actual. But overall the tendency between amplitude and spectra were similar.

　　For breaking three wave cases, the amplitude of lower sideband frequency was selectively amplified through the breaking process. Before the wave breaking, the surface elevation and the spectra were consistent with the measured results just such as non-breaking cases. After breaking the evolutional tendency of numerical simulation didn’t matched with experimental data, was reasoned to the unconsidered breaking effect and the incorrect energy translation. The simulation also was compared with the three wave cases include breaking effect by an additional proper damping function. The results showed that the phenomenon about amplitude of lower sideband frequency was selectively amplified through the breaking process. It was expected due to the limited knowledge of wave breaking in deep water. However, the comparison of dimensionless amplitude exhibited the qualitatively matched well, but the quantitatively about describing the energy translation and the evolution after a series of breaking still needed to be researched in the further.

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