- 學位論文
海岸地形變遷數值模式
Numerical Modelling for Coastal Morphodynamic Evolutions
摘要
在以往海岸地形變遷模擬案例發現，基於二維平面水深積分平均流場配合總漂砂量公式之海岸地形變遷模式在碎波帶內往往無法準確模擬，主要原因為碎波帶內底床上方存在一水下逆流所致，加上長期地形變遷模擬常於碎波帶內發生數值震盪情形，因此實有必要針對上述問題進行整體海岸地形變遷模式改良。 整體海岸地形變遷模式包括四部分：波浪傳遞模式、水理流場模式、海岸漂砂模式及地形變化模式。在波場模式部分，本文基於解析碎波前後高非線性問題及碎波後再生波回復的解析，以Nwogu(1993)所推導以任意水深形式表示之二維布斯尼斯克方程式為基礎，並加入Kennedy et al. (2000)建議利用水位時變率作為碎波及回復波指標，建立適用於模擬在近岸海域任意變水深地形下之平面波場模式。而流場模式方面，本文主要以前述平面水深積分平均流場模式為基礎，配合1DV 模式架構擬三維(quasi-3D)的流場數值模式，剪應力項以平面二維波流場模式計算結果之波高、碎波波能消散及平均水位分布等呈現，並與前人研究成果進行驗證結果良好，顯示本文發展之擬三維流場模式之正確性及準確性。海岸漂砂量模式方面，為發展可分析水深方向不均特性的漂砂量公式方面，本文將總漂砂量分為懸浮載與底床載，分析過程中並引入波浪近岸傳遞的不對稱性及沙漣存在的影響，並藉由非線性波理論將相關待定係數公式化增加應用範圍，最後並與前人實驗結果及知名漂砂公式進行驗證。而地形變化模式改良部分，本文首先探討數值震盪原因後，發展每一時階漂砂量隨底床坡度修正之二步驟三時階WENO海岸地形變遷數值模式，精度可達O( )。模式建立後針對實際現場複雜海岸進行驗證結果良好。 整體模式建置完成後，利用DHI之LIP11D動床沙洲遷移實驗結果進行驗證，並應用於符合暴風型海灘條件等坡度理想平直海岸沙洲生成模擬，顯示本文發展模式之可行性與實用性。最後並以和美漁港防波堤減量實例計算碎波帶內港口附近侵淤情形並與實際監測結果比較結果良好，顯示本文所發展模式在實際海岸地形預測具高精確度及可信賴度，未來可供國內海岸保護規劃、港灣工程及大型海岸開發海岸地形變遷評估分析之用。
並列摘要
Coastal morphological models are indispensable and powerful tools that allow harbor and hydraulic engineers to predict coastal bathymetry, to analyze the impact of coastal structures, and to verify the planning and design of harbors and coastal defenses. Morphological models are based on various sub-models for waves, nearshore currents, and sediment transports, coupled with the sediment transport model. The morphological model solves the sediment conservation equation to calculate bed-level evolution. The local sediment transport is first calculated by waves and nearshore currents sub-models, and the bed form evolution is then computed based on the conservation of sediment and its continual redistribution in time. The objective of the research is to develop a new numerical model of coastal morphodynamic evolutions. In the wave sub-model, the Boussinesq equation is employed to develop a series of numerical calculations to simulate the affection of wave height changes in the nearshore area. In the wave driven current sub-model, the quasi-three-dimensional numerical model of nearshore currents is developed by modified 2HD depth-averaged two-dimensional model with wave surface roller system and extended 1DV vertical velocity profile model to describe the undertows in the surf zone. In sediment transport model, there are quasi-steady, practical formulas, to predict the sediment transport rates based on modified bedload and suspended load in wave, current or wave-current interactional conditions that are characteristic of the waves asymmetry and nonlinearity. In the coastal morphological model, the bed-slope updating techniques, WNEO schemes, and 2-step with 3-time-level temporal discretization schemes are employed to remove oscillations and improve the stability with accuracy up to are developed. Finally, the integral models show good performance for LIP11D sandbar experimental data by DHI, the formation of sandbar for ideal cases, and real coastal areas with complex topography and the influence of coastal structures.
參考文獻
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