前導下沉N型波下速度場之探討

Abstract

本文旨在利用高速攝影機及高強度LED建立一低成本之PIV量測系統，並使用本研究室長20 m、寬0.34 m、高0.5 m之二維推板式造波水槽進行造波，用以量測前導下沉N型波作用下之速度場。首先以孤立波實驗進行實驗設置的驗證，針對孤立波的傳遞過程，對其速度場以不同實驗條件之波高水深比(H/h=0.086、0.127、0.166)進行速度場之分析。並以PIVlab分析實驗結果，再與前人所提出的解析解理論和開源軟體OpenFOAM的數值結果進行比較，比較後發現PIV量測結果與解析解還有數值結果都非常貼合。同時利用可視化的方法針對其粒子軌跡，進行定量及定性的分析。 在眾多N型波研究中，相較於孤立波已有較完整的速度場理論，N型波並沒有速度場之解析解。此篇文章將以PIV量測方式提供前導下沉N型波傳遞下之速度場的實驗數據結果，以利後續相關的研究做為實驗數據參照。由實驗結果可發現N型波於水平速度場和垂直速度場，在深度上的變化與孤立波相似，隨著初始水深越淺，垂直速度有遞減的趨勢。但在時間相位的變化上，本文所研究之N型波，則因其前導下沉及尾波的特徵，相較於孤立波恆為正的水平速度，其具有負方向上的水平速度。我們也以可視化的方法將N型波的粒子軌跡與相對應波高之孤立波粒子軌跡進行比較與分析，可發現針對不同條件的N型波，其粒子軌跡會有漩渦狀收斂以及繼續向後飄送兩種結果，且兩種結果中其最大垂直方向位移皆略大於相對應波高之孤立波之最大垂直位移。 最後本文針對不同實驗條件的N型波下之速度剖面，驗證其是否滿足長波理論。結果顯示，本研究所探討的N型波案例，其速度剖面與長波理論下的速度剖面有非常好的貼合，此結果也說明了N型波做為海嘯替代模型的適用性。

The purpose of this study is to establish a low-cost PIV measurement system using a high-speed camera and a high power LED source. The experiments were conducted in the 20m long wave flume using a piston-type wavemaker, and to analyze the velocity field of the leading-depression N-waves. First of all, we verified the experiment setup by analyzing three different wave height-to-depth ratios (H/h=0.086、0.127、0.166) of the solitary waves propagation process. The PIV experimental results are compared with existing theories and the numerical results of OpenFOAM, and we found that the experimental data are in close agreement with the analytical solution and numerical results. The quantitative and qualitative analysis of the particle trajectories are also performed by visualization methods. Compared with solitary waves, there is a relatively complete theory, but in many studies of N-waves, there is no analytical solution of the velocity field for N-waves. This study will provide the experimental data results of velocity field under the leading-depression N-waves propagation by the PIV measurement as the experimental data reference for related research. Experimental results show that the variation of the horizontal and vertical velocity profile in depth is similar to solitary wave. But for the variation in time phase, compared with the constant positive horizontal velocity of the solitary wave, the N-waves in this study has a negative horizontal velocity. Meanwhile, we also compare the N-waves particle trajectory with the solitary wave particle trajectory of the corresponding wave height by visualization methods, the results show that N-waves have vortex convergence and drifting forward two phenomena under different condition, respecticely. And the maximum vertical displacement of N-waves is slightly larger than the maximum vertical displacement of the solitary wave of the corresponding wave height. Finally, in this study we verify whether the velocity profiles of N-waves under different experimental conditions satisfy the long-wave theory, and the results show that the velocity profile of N-waves in this study is in close agreement with the velocity profile under the long wave theory, which also illustrates the applicability of N-waves as an alternative model for tsunamis.