大氣卡門渦街中的三維渦管結構

Abstract

根據Helmholtz的理論，渦管在流體中不能斷裂。令我們感興趣的是：在大氣中的卡門渦街有許多渦管，他們的三維結構如何？是否彼此獨立？我們利用理想模式來探討這個問題。我們在VVM（Vector Vorticity Model, 預報渦度場而非動量場的模式）置入初始逆溫層和鐘型地形，考慮無地表摩擦，利用輸出之三維渦度場來檢視地形附近以及下游拖曳出來之渦旋的渦管結構。 實驗顯示山後方的垂直渦管是從水平渦管扭轉出來的，這些水平渦管可視為通過圓柱之水平流場隨高度的變化，對過去研究透過斜壓產生的機制提供另一種解釋。隨著時間發展，下游拖曳出來的垂直渦管由許多水平渦管串聯在一起，這些水平渦管的上升運動區可能與衛星雲圖上的雲區相符。我們也探討了Helmholtz理論在層化流體中的適用性，並藉由電磁學和動力學之間的類比和實驗來幫助我們了解此處渦度線的形式。最後做了此現象對風速、山高以及逆溫層強度的敏感度實驗，在模擬中發現渦街有破裂的形式出現，也討論了無因次參數bulk Froude number在模擬和實際個案的差異，可能受到探空時間與地點的影響。我們期望這些觀點可作為研究氣流過山產生的渦旋間交互作用的出發點，並在檢視衛星照片時能由雲的形式注意到逆溫層附近的水平渦度或者破裂渦街出現的可能。

According to Helmholtz’s theorem, vortex tubes cannot end in a fluid. Our interests lie in: how are the vortex tubes constructed in atmospheric von Kármán vortex street? Whether the vortex tubes are independent to the others? This issue is examined by an idealized model. Three-dimensional structure of vortex tubes is surveyed in the neighboring of mountain and downstream shedding by the simulation of VVM (Vector Vorticity model, which predict vorticity field instead of momentum field) with an initial inversion cap, a bell-shaped mountain and no surface friction. The simulation shows the initial vertical vortex pair behind the mountain is tilted from the horizontal vortices, which can be explained by the two-dimensional flow field past a cylinder differing with height, providing the baroclinic generation mechanism in previous study more explanation. The shedding parts are connected by horizontal vortices, of which the regions of upward motion may fit the cloud regions on satellite images. Besides, we used a craft to demonstrate the vortex lines by the analog between electromagnetics and dynamics. Finally, the sensitivity tests were conducted with wind speed, mountain height and inversion strength. We found the vortex street may be broken in our simulation. Bulk Froude number is also discussed in the simulations and observations, the difference may come from the timing and location of the sounding. We anticipate this point of view to be a starting point for research about interactions between two or more vortices generated by flow past mountains, and the horizontal vorticity or broken vortex street can be aware of by the clouds when examining a satellite image.