隨沿岸流所驅動的陸棚環流：挾帶過程與Arrested Topographic Wave

Abstract

從一些數值研究和少數的實際觀測中可以發現到，當河水注入到陸棚上，於海洋形成沖淡水鋒面結構及後續持續發展的沿岸流同時，沿岸流以外的周邊常能觀察到一與沿岸流流向相反且較弱的速度結構 (後續稱作reverse flow)，通常還同時伴隨向岸方向的速度。為了想探討reverse flow與沿岸流間的連結，本研究中透過三維海洋模式ROMS進行改變不同底床坡度、沿岸流流量，以及改變密度差的數值實驗，而在所有的模擬結果中，緊鄰沿岸流邊界的區域皆能成功發展出如前述的reverse flow速度特徵 (v < 0, u > 0)。其中，能發現到跨岸方向的寬度會隨著沿岸流的下游方向越寬，從所有結果的比較也能注意到寬度有隨坡度減緩而變寬的趨勢，而reverse flow強度與沿岸流傳遞速度呈正相關。經分析後發現reverse flow的結構特徵大致上能以 Arrested Topographic Wave (ATW) (Csanady, 1978) 理論做解釋，結果也顯示沿岸流邊界上透過混合而挾帶海水的過程 (entrainment processes) 為驅動reverse flow的主要因素。另外也發現到沿岸流邊界上的海水面梯度量值 (|dζ/dx|)，和被挾帶進沿岸流中的體積傳輸成正比，此關係更顯示了朝沿岸流邊界下凹的海水面是由於挾帶海水過程所導致的推論正確性。而應用到實際海岸中，若能取得周邊海水面梯度的觀測值，勢必能以ATW理論重製出reverse flow的海水面及速度結構。 此外，該理論有助於我們了解reverse flow對於單一因素改變下的反應，如寬度受底床坡度影響的關係也可以渦度平衡角度進一步解釋，當我們在沿岸流邊界上固定一相同 dζ/dx，於坡度越陡時，渦管向近岸受擠壓而產生的負渦度趨勢越強，同時則需要較強的正渦度趨勢來維持守恆，理論顯示為由底床應力旋度所產生。設置相同的 dζ/dx 即為在邊界上固定相同的reverse flow速度峰值，因此，所對應reverse flow的底床應力若分布於較窄的寬度上則會使速度梯度 (dv/dx) 較大，等同於產生較強的正渦度趨勢。

Prior modeling studies and limited observations have found that, as riverine sources enter continental shelves to form buoyant plumes and coastal currents, there often exists a weak current seaward of the buoyant outflows. This weak current flows primarily in the direction opposing the buoyant outflows (termed reverse flow hereafter) and is onshore-directed. To explore the linkage between the reverse flow and coastal current, we conduct numerical experiments using ROMS, with different bottom slopes, river discharges, and density contrasts. In all experiments, a robust reverse flow, characterized by upshelf and onshore velocity (v < 0, u > 0) is observed along the coastal current boundary and further downshelf. The cross-shore width of the reverse flow increases with downshelf distance. Among the cases, the maximum reverse flow width increases as the bottom slope decreases, whereas the reverse flow magnitude is positively correlated with the coastal current propagation speed. We find that the reverse flow structure can largely be explained by the theory of Arrested Topographic Wave (ATW) (Csanady, 1978), and there are indications that the reverse flow is driven by entrainment processes. A peak sea-level gradient (|dζ/dx|) is found at the seaward boundary of coastal current, with its magnitude scaling positively with the volume entrained into the coastal current. This suggests that the negative sea-level anomaly at the boundary is generated by coastal current entrainment. Using the observed dζ/dx as a forcing, the ATW solution can reproduce the spatial distribution of sea-level and velocity in the reverse flow. Furthermore, the sensitivity of reverse flow width to bottom slope can be interpreted in terms of vorticity balance between bottom stress curl and vortex stretching due to onshore flow across sloping bottom (i.e. the topographic beta effect).