急速加深之海洋混合層中Langmuir 環流的流場結構

The Structure of Langmuir Circulation in the Rapid Deepening Stage of the Mixed Layer

陳世明(Shi-Ming Chen)

指導教授 ： 蔡武廷 ； 葉克家

國立交通大學/工學院/土木工程系所/博士(2015年)

https://doi.org/10.6842/NCTU.2015.00181

摘要

本研究應用大渦模擬探討Langmuir環流（LC）在一真實暴風事件中，其流場結構與因風速上升和波浪增大而急速加深的混合層間的交互作用，並採用Craik-Leibovich方程式來參數化LC。Craik-Leibovich方程式主要由vortex force項來控制LC強度，此項代表波浪與紊流場之間的交互作用。為了解vortex force強度以及密度分層強度對LC結構的影響，除了以原本真實事件觀測資料推估之物理參數，另再以調整過的波浪參數和垂直密度梯度來進行數值實驗，包括一完全無浪的極限情境。模擬結果顯示，LC明顯促進紊流的垂直混合效應，產生較為均勻的混合層流場。若以紊流動能的觀點來看，LC會增強接近水面處的橫向紊流動能，且垂直向紊流動能的最大值（約位於水下0.1倍混合層深度處）也會增強。分析紊流動能變化率可知在LC的影響下，波浪引致之流場不穩定是接近水面處紊流動能的主要來源，異於主要由剪紊流場之不穩定來產生紊流動能的風剪力邊界層。混合層的加深也會受益於LC，而其影響的程度跟密度分層強度成反比。
Langmuir環流的特徵還包括水面橫向聚合條痕，這些條痕肇因於水面下成對反向旋轉的渦旋管結構。水面主要條痕的間距可由頻譜分析來量化。而藉由一結合條痕辨識和條件採樣的方法，我們可獲得水面下具代表性且清楚的流場結構，並量化Langmuir渦旋管的橫向及垂向長度。在LC主導的流場中（紊流Langmuir數Lat介於0.3和∞之間），主要條痕間距約為渦旋管橫向長度的兩倍，證實水面條痕確為LC所致。而LC在發展的過程中，其渦旋管的尺寸與混合層深度有密切關係，因混合層底部的密度躍層會阻礙渦旋管向深處發展。若混合層深度足夠，密度躍層不影響渦旋管的發展，則渦旋管本身會具有相似的橫向和垂向長度，其形狀寬深比值接近於一。相反地，若混合層非常淺且底部的密度分層非常強，則渦旋管無法向下穿透底部密度分層，導致流場垂向發展被擠壓，呈現出寬度大於深度的渦旋管形狀。本研究藉由數值實驗，建立水面條痕和水下流場結構的關聯性，以及展示Langmuir渦旋管擴大和混合層加深過程中的交互作用，指出Langmuir渦旋管並無一定的寬深比值，因其發展受混合層深度以及底部之密度分層強度影響。

關鍵字

海洋混合層 ； Langmuir環流 ； 大渦模擬 ； Craik-Leibovich方程式 ； 環境 物理紊流 ； 紊流條痕

並列摘要

An oceanic mixed layer of an observed storm event that is featuring growing wind/surface waves and a rapidly deepened mixed layer is realized with threedimensional large-eddy simulations to study interactions between Langmuir circulation and the mixed layer. Langmuir circulation in the simulations is parameterized with Craik-Leibovich equations that a term of vortex force in the momentum equations, representing the interaction of wind-induced shear currents and the wave fields, controls the strength of Langmuir circulation. Numerical experiments are conducted as well by varying the vortex force and strength of stratification for the reason to understand how the strength of vortex force and stratification influence the structures of Langmuir circulation, including an extreme scenario for a no wave condition. The simulation results show that strong vortex force induces more homogeneous mean velocities through the mixed layer, suggesting enhancement in turbulent mixing. In the perspective of turbulent kinetic energy (TKE), Langmuir circulation could intensify the TKE crosswind component near the water surface and also the vertical component at around 0.1 times mixed-layer depth. By analyzing TKE budget, reduced shear production and increased Stokes production are revealed near the water surface. It suggests the primary source of near surface TKE for the flows influenced by Langmuir circulation is Stokes shear, rather than wind-driven shear which is the main source for pure shear boundary layer flows. Langmuir circulation also enhances deepening of the mixed layer, and the extent of influence of Langmuir circulation on mixed-layerdeepening is negatively correlated to the strength of stratification.
One predominant feature of Langmuir circulation is the streak of crosswind convergence at the water surface, which is generated by the underlying structure of counter-rotating vortex cells. Through the spectral analysis in terms of crosswind velocity near the water surface, the dominant streak spacing is quantified. Also a method combining the surface streak detection and conditional average algorithm is employed to evaluate the lateral width and penetration depth of a conditional-averaged Langmuir cell. For the cases of Langmuir-turbulence-dominant flows (turbulent Langmuir number Lat ranges from 0.3 to ∞ ), the dominant streak spacing approximates twice the lateral width of the Langmuir cell, indicating a pair of cells reside between successive dominant streaks. The quantified cell width and depth correlate to the mixed-layer depth since the pycnocline below the mixed layer can hinder penetration of the Langmuir cell. The Langmuir cell exhibits similarity of the cell width and depth when the mixed layer is deep from blocking the vertical extending of the cell. Other than the unconstrained condition, the cell could be squashed vertically by a very shallow mixed layer with extremely strong stratification. Thus it leads to a laterally stretched Langmuir cell with an aspect ratio (width to depth) larger than one. From the analyses of the numerical data, this study depicts the connection of surface streak signatures and the underlying Langmuir circulation structures, and the relation between Langmuir cells and the mixed layer in distinct conditions. It therefore suggests that there is no specific aspect ratio of the Langmuir cell and that the shape of the cell depends on the mixed-layer depth and the stratification in the pycnocline.

並列關鍵字

oceanic mixed layer ； Langmuir circulation ； large-eddy simulation ； Craik-Leibovich equations ； geophysical turbulence ； turbulent streaks

參考文獻

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