A Study of Viscous Wave Propagating over Uneven Seabed

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基本資料

Project title

Code/計畫編號

NSC100-2221-E022-006

Translated Name/計畫中文名

黏性波浪在不規則底床上之運動

Project Coordinator/計畫主持人

Chia-Cheng Tsai

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Marine Environmental Engineering,NKUST

Website

https://www.grb.gov.tw/search/planDetail?id=2324487

Year

2011

Start date/計畫起

01-08-2011

Expected Completion/計畫迄

31-07-2012

Bugetid/研究經費

543千元

ResearchField/研究領域

海洋科學

台灣本是一個海島型的國家，地狹人稠且土地利用有限，所以海洋環境的利用與國土的保護相形重要。然而欲了解海洋中之物理現象則首重波場運動，因此建立理論及數值模式模擬波場運動現象，可有效提供工程規劃、預警防災、國土保育與休閒遊憩等參考。往昔描述波浪變形效應大多採用勢函數所表示之控制方程式，如緩坡方程式、淺水波方程式、布斯尼斯克方程式等等。然而這些方程式通常都假設滿足質量守恆與能量守恆的原則下，而且是不可壓縮、非旋性、非黏性之流場，並以滿足拉普拉斯方程式為主架構各自發展解析波場運動的數值模式。近來隨著計算機的突飛猛進，波場分析漸漸採用可描述真實流體之納維爾-斯托克斯方程式來計算，雖然可詳細分析細部波流場變化，同時考量實際物理現象如黏滯性、張力、剪力等，但在計算大範圍區域仍屬耗時。因此利用緩坡方程式計算大範圍的優勢，並結合真實流體含黏滯性之特性，進而延伸緩坡方程式的適用性，使其更具競爭性與時效性。為驗證本模式之應用，在此將以間接特徵函數展開法(IEMM method)所得之解析解來做交互比對。有關間接特徵函數前進展開法解析水波與階梯底床交互作用的問題，主要是利用在階梯上以水平速度表示的前進條件，求解以水平速度表示的未知係數線性方程組，進而得到波場資訊。另外，此法對於一系列階梯底床地形之交互作用也能夠正確求解，而且此法對和緩或是陡峭的曲線地形上，計算收斂性較優於轉換矩陣法（TM method）。本計畫的主要目的是在推導一含黏滯性效應之新型態緩坡方程式，有別於傳統勢能流架構下之理論，以其符合真實流體波動之現象。同時與解析解(IEMM method)做比對並驗證模式可性度。再者，針對代表性之底床地形進行水工試驗並與模式結果做交互比對驗證。最後，綜合上述研究成果分析並加以討論發表於國際期刊上。關鍵詞：納維爾-斯托克斯方程式，黏滯性效應，緩坡方程式，間接特徵函數前進展開法，轉換矩陣法。 It is well known that environments of the ocean are usually concerned for an Island country in the world. In the ocean, there are so many physical phenomena interesting us. However, the most important phenomena are wave propagation and dissipation. For analyzing wave motions, to develop theory and to establish numerical model will be a reliable way for engineering applications. There are several models to analyze wave transformation such as the mild-slope equation, shallow-water wave equation and Boussunesq equation and etc. All of these models are based on irrotational, incompressible and inviscid assumptions. Basically, they also satisfy the Laplace equation since the conservation of mass and the conservation of energy. However, the characteristic of potential flow is different from real flow due to the exists of viscosity, surface tension, and shear stress. Generally, using Navier-Stokes equation to model wave propagation is the best way, but it still need much computing time for large area. In other words, using mild-slope equation to model wave propagation is a good alternative in the applications of coastal engineering. For this reason, a new kind of mild-slope equation with viscous effect will be derived from Navier-Stokes equation. To validate this new model, an indirect eigenfunction marching method (IEMM) is developed to provide step approximations for water wave problems. The bottom profile is in terms of successive flat shelves separated by abrupt steps. The marching conditions are represented by the horizontal velocities at the steps in the solution procedure. The approximated wave field is thus obtained by solving a system of linear equations with unknown coefficients which represents the horizontal velocities under a proper basis. The results demonstrated that this solution is exactly reduced to the transfer-matrix method (TM method) for a specific setting. The combined scattering effects of a series of steps can be described by a single two-by-two transfer matrix for connecting the far-field behaviors of both sides for this method. The solutions obtained by the IEMM are basically exact for water wave problems considering step-like bottoms. Numerical simulations were performed to validate the present and commonly used methods. Furthermore, it also shows that the solutions obtained by the IEMM converge very well to Roseau's analytical solutions for both mild and steep curved bottom profiles. The present method improves the converges of the TM method for solving water wave scattering over steep bathymetry. The main purpose of this program is to develop a new kind of mild-slope equation with viscosity for modeling the motion of real flow water wave. This model can be verified with analytical solutions of the IEMM and the results of the conducted experiments. Moreover, the results of the present project will be published in international journals. Keywords: Navier-Stokes equation; Viscosity; Mild-slope equation; Indirect engenfunction marching method; Transfer-matrix method

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A Study of Viscous Wave Propagating over Uneven Seabed

基本資料

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