非線性內波在南海北部大陸棚傳遞之模擬

Abstract

根據以往的衛星影像顯示，南海北部的大陸棚區為非線性內波活動頻繁之處，當非線性內波進入大陸棚後，會因水深改變或遇到障礙物有折射、反射及繞射的現象。一張衛星影像中經常會出現許多群的非線性內波群，但往往無法分辨出哪些非線性內波群為同週期或是同一源頭。假如有連續的衛星影像，就可以追蹤同一個非線性內波群在不同時間的位置，也可依照波源的位置、產生機制、與潮汐的相位關係等等，將非線性內波群分類。但是，現在沒有連續的衛星影像，全面追蹤非線性內波在大陸棚上的傳遞，或者採用數值模擬的方法，都可以將內波群分類。全面追蹤是可望而不可及的方法，因為它需要太多的儀器設備及海上作業時間，所以本研究採用數值模擬的方法，估算非線性內波傳遞的方向與速率，及波前位置隨時間的改變，以利在一張或數張衛星影像當中找出同一起源，且產生時間相差一個週期的非線性內波。在模擬非線性內波在兩層流體的傳遞速度時，都需要給定非線性內波的振幅和兩層流體的厚度。由於一般情況下只有衛星資料而沒有現場資料，內波的振幅和兩層流體的厚度都無法決定，因此本文利用歷史水文資料推算線性內波第一斜壓模態的速度，利用衛星影像中的亮帶和暗帶之間的距離，再根據KdV (Korteweg - de Vries) 理論推算非線性內波振幅，進而求出整個區域之非線性內波在大陸棚上傳遞速度的分布，以模擬非線性內波在大陸棚上傳遞與折射的情形。並使用OSU (Oregon State University) 的正壓潮流模式，以估算正壓潮流對內波傳遞所造成的影響。本文模擬非線性內波傳遞路徑的方法，受限於缺乏現場的連續觀測資料，無法估算平均流、高非線性效應、非線性內波半寬隨水深的變化…等等的影響。經過分別比較模擬結果與單張衛星影像、與同一天不同衛星影像、以及與連續兩天衛星影像，驗證此方法可以估計非線性內波波前位置隨時間的改變。本方法，還可將一張衛星影像中，同週期且同起源之非線性內波群歸類，或者尋找影像中不明顯的非線性內波，以及其前一週期波前之位置；也可在不同時間的衛星影像中找出同一個非線性內波。估計波前位置的誤差平均0.04%，標準誤差為5.1%。

Satellite images show that nonlinear internal waves (NLIWs) often exist over the continental shelf of northern South China Sea. When NLIWs enter the continental shelf or encounter bathymetric changes, they will be refracted or diffracted by the change of water depth or be reflected by the obstacles. It often happens that many groups of NLIWs in one satellite image that makes one difficult to distinguish the NLIWs groups that were generated periodically from the same source and from the same generation mechanism, but with 24 hours lag. These NLIWs may be in one or many different satellite images. Tracing the same group of NLIWs will not be a problem if one has consecutive satellite images at short time lags. Without consecutive images, categorizing groups of NLIWs requires ability to predict propagation speed and path of NLIWs over the continental shelf. Because the propagation speed of NLIW (Cn) depends on the stratification, water depth, tidal and mean currents and NLIW amplitude, archived CTD data of April and May in 1995-2001 were used to derive the first baroclinic mode of internal semi-diurnal tide over a grid of 60 by 90 points. Without in situ data on the NLIW amplitude which enhances NLIW propagation speed, satellite images over the shelf are used to estimate the half-width of NLIW fronts and then derive the NLIW propagation speed with KdV (Korteweg - de Vries) theory. Then, simulation of the propagation and refraction of NLIW fronts may be done with Snell’s law. The effect of barotropic tidal current, which is predicted by the tidal model of OSU (Oregon State University), was included in the prediction, but the effect of mean current is ignored because it is much smaller than Cn. Predicted propagation of NLIW fronts were successfully in categorizing NLIWs in one or two consecutive satellite images, even from different satellites. The accuracy of predicted distance, or the mean predicted propagation speed Cn is on the average of 0.04 % with standard deviation of 5.1 %. This accuracy of predicted Cn seems to be better than those derived from mooring data in ASIAEX.