颱風邊界層震波狀結構探討

Abstract

Williams et al. (2013)使用軸對稱垂直平均邊界層模式，說明在渦旋 徑向動量方程式中u@u @r 項可以在颱風邊界層內風場產生具有高梯度特 徵的震波狀結構(shock-like strucuture)。這些震波狀結構會伴隨強而集 中的上升運動，正是我們一般用來定義眼牆的位置。然而，觀測顯示 這些震波狀結構可以是非軸對稱的過程，因此探討非軸對稱的震波狀 結構是相當重要的議題。 本研究將Williams et al. (2013)所使用的軸對稱垂直平均邊界層 模式改寫為卡式座標係，空間微分採用Double Fourier pseudo-spectral method。並結合正壓模式，試圖探討非軸對稱的震波狀結構在颱風邊 界層中的生成過程。 實驗結果發現，正壓模式中非軸對稱的渦度帶可以在垂直平均邊界 層驅使出相對應的非軸對稱震波狀結構，並透過軸對稱化過程，最終 將形成近似同心圓的結構。分析發現這些震波狀結構所產生的上升運 動與Ekman pumping的強度相差一個數量級以上。 最後，我們也試著考慮加入反饋過程，使得邊界層內所產生的上升 運動可以加強該處在正壓模式中的渦度。結果顯示反饋過程將幫助細 絲渦度帶重整，組織成更強的渦度帶，有助於雙渦交互作用後，使拉 伸(straining-out)的渦旋形成雙眼牆結構。

Williams et al. (2013) used an axisymmetric slab-boundary layer model to demonstrate that the u@u @r term in the radial equation of motion produces a shock-like structure in the tropical cyclone boundary layer radial wind. These shock-like features are one of the essential ingredients of a hurricane vortex with a well-defined eyewall updraft structure. However, the formation of these shock-like structures may be an asymmetric process based on observations. Therefore, it is necessary to study the asymmetric process of shock-like structures formation. In order to discuss the asymmetric process of shock-like structures formation in tropical cyclone boundary layer, we modified the axisymmetric slab-boundary layer model into a two-dime- nsional model, which is coupled with barotropic model in Cartesian coordinate by using double Fourier pseudo-spectral method. We find that asymmetric vorticity structures in barotropic model could produce corresponding asymmetric shock-like structures in slab-boundary layer model, and eventually form the concentric structures through axisymmetrization. The updraft generated by shock-like structures is demonstrated to be an order larger than Ekman pumping. Feedback process is also considered such that the boundary layer pumping is able to enhance the vorticity in barotropic model. Our results show the feedback process could reorganize the vorticity, leading the straining-out vorticity to form a concentric eyewall.