波浪通過矩形潛堤：堤寬對諧和波生成影響之實驗研究

Surface Waves Propagate over a Submerged Step : The Effect of the Width of Step on Harmonic Generation

李芳承(Fang-Cheng Li)

指導教授 ： 丁肇隆

國立臺灣大學/工學院/工程科學及海洋工程學研究所/博士(2013年)

https://doi.org/10.6342/NTU.2013.02430

摘要

本文藉由在台大工程科學暨海洋工程所基礎流力實驗室中的斷面造波水槽，應用造波系統配合高速攝影技術與光學系統拍攝一系列波浪通過台階式結構物的波浪影像，再利用影像處理技巧進行邊緣偵測，數位化、分析波浪連續自由液面高程。其中從全尺度拍攝中，成功地利用LabVIEW發展多斷面影像連結技術與邊緣偵測技術，藉由量測Y軸向放大影像觀察所波浪通過潛堤細部物理特徵現象，同時，數位化水面高程資料，透過Matlab發展二維快速傅立葉轉換(2DFFT)結合一維Morlet小波轉換(1DMWT)方法完整分解波浪訊號。
由於高速攝影機進行多斷面全尺度波浪液面量測方法，取樣速度快且空間解析度高，所以優於一般低取樣數的CCD量測與傳統波高計量測，由Y軸向放大影像和連結結果，所得到連接面誤差低於2像素(Pixel)，且在時間軸上幾乎可達無誤差。另外，本文提出的方法，更可以分解任意不同水深條件下，波浪通過構物之入反射波、高階諧和波與自由波和強迫波訊號，對於分析波浪複雜的非線性交互作用現象具有相當的實用性，作者所發展的方法也得到良好的驗證。
實驗研究針對波浪過不同堤寬Bx之矩形潛堤探討其高頻諧和波生成影響，透過能量通率(E*Cg) 空間分佈計算，在能量(振幅)與能通量(E*Cg)觀點下，將結果進行最佳化參數，利用入射波條件Ur.數並引入 〖〖(B〗_x/λ_i)〗^(±n)參數，訂定出以二階諧和波生成門檻值，分析結果得到n=0.09；再以能通量觀點，其中強迫波與自由波能量生成，分析結果得到分別n=+0.39與n=-0.32。研究中也針對主頻率與二倍頻空間振幅關係，提出一組數學方程組模擬，空間上模擬因摩擦效應振幅曲線中的衰減率，不能忽視。最後探討，探討波浪通過潛堤時，在Step1與Step2 所造成之反射率、透射率與能量消散影響。本實驗結果相當具可信度與參考價值，可提供數值模式發展研究者，進行比對驗證之。

關鍵字

2DFFT ； 1DMWT ； 高階諧和波 ； Ur.數 ； 能量通率(E*Cg)

並列摘要

This study used wavemaker system and high speed camera tech with optical system to take wave passed over a step construct images at the fundamental fluid mechanics lab, department of Engineering Science and Ocean Engineering, NTU. And used the image processing techniques with edge detection and digitize to analysis the free surface elevation. In the Full-scale image, using LabView successfully developed multi-section image connection technique with edge detection. By measuring enlarge Y axis image to observe the physical phenomenon details when the wave passed over the submerged dike, at the same time, the digital free surface data could be totally analysis the wave phenomenon by using Matlab to develop 2DFFT and 1DMWT.
Multi-section Full-scale measure techniques by using high speed camera, it's better than the low sampling CCD camera and wave gages because of its higher sampling and space resolution. The enlarge Y axis error is less than 2 pixels at connecting surface, and almost no error at time. Otherwise, the propose method could decompose the waves of incident, reflect, even the free and bound wave of higher harmonics. By this method also useful to deal with the complex nonlinear harmonic waves interaction and had been good validation.
Finally, this study focused on research the effects of generating higher harmonics waves by different width (Bx) of step obstacle.The point view of energy(amplitude) and energy flux(E*Cg) by determining the spatial distribution of energy flux(E*Cg) and take the result to parameter optimation. Setting a threshold of generated second harmonics wave by using incident wave Ursell number and introduced a parameter(Bx/λi)±n, n=0.09. And the viewpoint of energy flux, the results were obtained n=+0.39 and n=-0.32 at generating bound wave and free wave. In this research also bring up a simulation of math model to describe the relationship of spatial amplitude between first and second harmonics. At the simulation spatial domain, the curve decay rate of amplitude can't be neglect because the friction effects. At the last, we discussed the effects of reflect(Kr)、transmission(Kt) and energy dissipation(Kd) at Step1 and Step2 when waves propagate over a submerged. And our results were quite reliable and could be provided to numerical researchers to examine their models.

並列關鍵字

2DFFT ； 1DMWT ； Higher harmonics ； Ursell number ； Energy flux

參考文獻

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