南海北部強非線性內波之數值模擬

Abstract

由歷年衛星影像資料中顯示，南海北部的非線性內波運動十分頻繁，從東邊的呂宋海峽到南海西北邊的大陸棚區可以明顯的觀察到非線性內波訊號。關於南海非線性內波的研究多集中於南海大陸棚上，多數研究的結果推測南海北部非線性內波起源於南海東緣的呂宋海峽區域，但是對於非線性內波如何產生與演化、如何從深水區傳遞到南海大陸棚的研究相對較少，也尚未有明確的結論。 在2005年與2006年的內波起源實驗中，於呂宋海峽先後施放五組溫度計串錨碇進行短期的觀測，藉由量測海水等溫線隨時間變化的情形，研究非線性內波在此深水區中傳遞時隨距離演化的情形，亦由溫度計串錨碇上觀測到最大振幅約140公尺的非線性內波。在2007年同區域的實驗中，經過長距離追蹤內波的第一個波前，發現從表層以下，內波波形及振幅幾乎未改變，振幅和半高寬都很大，各層深度內波的振幅η與深度h的比值 η/h 接近於1，應該屬於強非線性內波。之後經過實測資料以及衛星影像的比較，發現此強非線性內波在118.5°E時已經演化為4個波前的波包，與過去資料的演化情形相當，但其空間尺度較2005及2006年的觀測資料來的大上許多，其半高寬 (L) 約為5.5公里，而推算出來的半寬 (Δ) 則為2.9公里。 當η/h~1時，一階弱非線性的KdV理論已經不能適用(Grue, 1999)，所以本研究採用數值方法來模擬南海北部發現之強非線性內波，數值模式使用完整非線性項的Navier-Stokes 方程式、擴散方程式及連續方程式。依照Liu (2006) 的推論結果，南海北部非線性內波的發生處位於呂宋海峽西側的恆春海脊位置，故在此處放置一內孤立波波前用以模擬其傳遞的過程。模擬結果顯現非線性內波的傳遞情形類似實測資料，數值模擬中的強非線性內波其半寬和振幅皆很大，隨著傳遞距離的增加同樣會產生波包演化的情形，而其波包演化的數目、時間、距離以及傳遞速度與過去的資料亦相當接近；例如，在恆春海脊西方100 km處，模擬的結果顯示非線性內波演化為3個波前，其傳遞速度約為2.76 m/s，與實測現象類似。 伴隨著電腦效能的提昇以及改進數值運算方法的效率，相信更好解析度的數值模式不僅在模擬的物理現象更真實，在內波形成過程的動力研究上，更可模擬非線性內波的形成過程。

Nonlinear internal waves (NLIWs) are very active in the northern South China Sea (SCS). Historical satellite images show that NLIWs appear often between Luzon Strait in the east and the continental shelf at northwest of SCS. Most of the researches of NLIW concentrate over the shelf of SCS, but not much on the propagation and the generation process of NLIW in the deep sea region of SCS. So far, lots of researches suggest that the source of NLIW is in the Luzon Strait, but there is no definitive conclusion about how it happens and where the locations of source regions are. In the field experiment to find the source of NLIWs in 2005 and 2006, total 5 T-strings were deployed in Luzon Strait for a week long observation. By the record of isotherm displacement during the passage of NLIW at different locations, we derived information on the evolution of NLIW (from single wave front to wave packets) west of HengChun Ridge, and found maximum amplitude about 140 m. In 2007 experiment, the focus was closer to HengChun Ridge and the NLIWs again have big amplitude (η) and large half-length from surface down to 500 m depth. The ratio of η to upper layer thickness (h) was nearly 1. They are categorized as strongly NLIWs, while KdV theory can only simulate the wave form and propagation of a weakly NLIW, i.e. η/h < 0.4 (Grue, 1999). From the analysis of field data and satellite images of these NLIWs, we found that the width between points of vertical displacement equal to half amplitude, is about 5.5 km, that is equivalent to half-width of 2.9 km, according to KdV theory. To account for the strong non-linearity of NLIWs, a fully non-linear Navier-Stokes equation, along with diffusion and continuity equations, are used to construct a numerical model studying strong NLIWs. Simulation starts with a solitary wave at the left side of the model that represents the source of NLIW and the location of HengChun Ridge (Liu et al, 2006). The model-simulated propagation of NLIW looks similar to that observed in the field, in the sense of (1) the propagation speed, amplitude and half-width of NLIWS, (2) the number of wave packets that increases with the distance of propagation, or the evolution of NLIW. With the advancement of computer technology and the improvement of numerical method, this numerical model may imitate the NLIW evolution with details and become a more powerful tool in studying the generation process of NLIW.