波流耦合數值及理論分析

Abstract

本研究為一系列探討波流耦合模式的流場。本篇以Mellor在2008年提出的輻射應力(稱M08)為研究起點。我們使用包含M08的SUNTANS (Fringer et al. [2006])來模擬離岸流。然而，我們希望可以發展出比以線性波更具真實性的輻射應力，其中我們考慮非對稱波的輻射應力，由結果卻發現使用相位平均的線性波與非對稱波的差異為一個基底常數。接著，考慮二階的Stokes非線性波，並為了表現出波峰波谷區間的差異性，我們採用半相位平均方式計算輻射應力，結果卻發現由線性波疊加的非線性波無法表現出此差異性。另一方面，我們對於M08將波流流速定義為常數感到懷疑，因此我們建置一個模式，來模擬由壓力梯度所驅動的波流耦合模式，我們將分別去計算波浪流速及整體的流速，再利用整體流速減去波浪流速得到一殘餘流速，而這殘餘流速即為波流耦合下所導致的波流速度。我們設置了一個簡單的理想平坦地形，透過此研究的模式，模擬出這個殘餘流速的分佈情形以及它所引起的自由水面的高度變化。結果顯示，殘餘流速並不為一個常數，而是一個具有週期性運動分布的流場，這個結果也成功的驗證了我們的懷疑。此外，我們並比較波浪流速和殘餘流速輻射應力，此結果也符合統御方程式的物理闡釋。在這研究中，我們已經初步完成此波流耦合模式的設置，並以驗證其正確性。

In this thesis, we study wave-current interactions using different approaches. We begin with the radiation stress by Mellor [2008] (M08). First, we use M08 in the SUNTANS model to simulate the rip current. In order to obtain the more realistic radiation stress, we examine the radiation stress using the asymmetric wave. However, the result is as same as that obtained from the linear wave but multiplying with a different constant coefficient, which is due to the phase-averaged method. In this regard, we develop a framework in which the half-cycle average is applied to the second-order Stokes wave, such that, individual characteristics of the crest and the trough can be represented. However, the result shows that the non-linear wave which is series of linear waves cannot show the skewness even with the half-cycle average. On the other hand, we are skeptical about all existing RS formulations that treat the wave-induced flow as a constant current. For this purpose, we develop a simplified 2DV hydrodynamics model to produce the wave-current flow field which is forced by the pressure gradient disregarding the wave shape. Using the model, we demonstrate that the RS-induced flow is a periodic, which is different from existing studies and confirm our hypothesis. Different contributions to the wave-induced current are also examined.