小島尾渦流之數值模擬研究

Abstract

本論文利用高解析度(500公尺)之數值模式(MITgcm)探討小島尾渦流的特性與機制，我們以綠島為實驗場所，其寬約為7公里。本研究針對島嶼形狀、水平擴散、對流項離散格式(advection scheme)以及水平解析度的變異做了測試，最終能得到最完善的模式配置。 前人針對流體流過圓柱體設計了數值模式及水潮的實驗，本研究藉由司特勞克數(St)以及雷諾數(Re)的關係說明我們的模式結果與前人結果相近。另外，兩次的現場觀測分別得到尾渦流擺動週期(約12小時)以及島後流場型態變化，現場觀測與模式結果吻合。另外模式模擬出的表面渦流型態也與衛星影像有相近的結果。 本研究顯示綠島尾渦流與馮卡門渦街為類似的現象，有以下原因(1)渦流擺動頻率與水平渦流黏滯係數的關係跟前人圓柱體實驗類似，(2)渦流特徵受到雷諾數大小影響，並且得以界定過渡期的範圍，(3)另外綠島渦流長寬比(aspect ratio)相近於馮卡門渦街之長寬比，故推側綠島尾渦流即馮卡門渦街。 尾渦流產生的反氣旋式渦泫會受到慣性不穩定的影響造成削弱的情形，因此，氣旋式渦泫相較於反氣旋是渦泫有較顯著的湧升流，進而造成低溫。在小島及強流的特殊條件下，相對渦度可大於10倍的科氏參數，因此慣性不穩定的成長率相當大。然而，慣性不穩定在本研究並無顯著的效應，推測原因(1)流體分層限制不穩定的發展及(2)慣性不穩定造成的回復力使渦泫得以維持型態。 本研究透過渦流動能守恆方程，估計綠島尾渦流的渦流動能轉換項，包括了正壓轉換以及斜壓轉換項。結果顯示上游能量主要是透過水平雷諾應力轉換成渦流動能(Eddy Kinetic Energy)，故在渦流形成的過程正壓轉換項為主要的能量轉換方式。 最後，本研究發現發生混合的區域為水平流切最大的地方，與前人在綠島後方觀測到的結果是一致的，而根據本研究模式之結果顯示，強勁的垂直流切主要是透過island shelf以及渦管傾斜的影響所致。強勁的水平流切受到渦管傾斜影響貢獻垂直分量至垂直流切，推測與混合效應以及高的紊流動能消散率有關。

Small island wakes such as the Green Island (~7 km) wakes are simulated via a high-resolution model, MITgcm (500 m). The effect of variety of island geometry, horizontal diffusion, advection scheme and the horizontal resolution have been investigated in our model, which help us to acquire the most appropriate setup for further analyses. Previous numerical and laboratory experiments for a flow pass a cylinder have similar results to our model with the Strouhal number vs. Reynolds number diagram. The comparison between the numerical model and the field observations are similar in terms of the shedding period ~12 hours, and wake patterns at near field. The surface signatures of the wake, including the near field recirculation to the shed eddies, are in accordance with the satellite imagery. Our model suggests that the mechanism of Green Island wakes is primarily a phenomenon of von Kármán vortex street. Investigation of the shedding frequency as a function of the horizontal explicit eddy viscosity shows analogous trend with previous water tank experiments. Furthermore, even though rotation and stratification are considered in our island wake scenario, the transition regime is still measurable. The island wake behaviors also greatly depend on Reynolds number (Re). In addition, the aspect ratio in our simulation is similar to the Kármán’s ratio. It indicates that Green Island wakes have analogous features to the von Kármán vortex street. The asymmetry of island wakes is a result of the inertial instability, which tends to destabilize the anticyclonic vorticity. Consequently, strong temperature drop associating with upwelling is more substantial in the cyclonic recirculation than the anticyclonic recirculation. In the scenario of small island (Green Island), strong upstream flow magnitude (~1 ms-1), the normalized vorticity (relative vorticity divided by planetary vorticity) tends to be larger than 10. As a result, the growth rate is large, meaning the instability will grow rapidly. However, the distortion of the anticyclonic recirculation is not as significant as previous studies. The defect of the inertial instability is presumably due to (1) stratification and (2) strong relative vorticity magnitude, which the restoring force may compensate the anticyclonic recirculation and consolidate the shed eddy. The wake generation of the von Kármán-like island wakes is studied by evaluating the eddy kinetic energy budget. The current shear in the lateral boundary is the major energy source to generate eddy kinetic energy via the horizontal Reynolds stress to eddy kinetic energy. Therefore, the importance of the barotropic conversion term prevails the baroclinic conversion term. Our model results suggest the hotspot of the strong vertical shear, which may result in turbulent mixing and is co-located with strong horizontal shear layer. We found the vertical shear is primarily sourced from (1) the island-shelf effect and (2) the tilting of the vertical vorticity component. Evidence from previous observations shows active overturning and high Turbulence Kinetic Energy (TKE) dissipation rate at the shear layer.