颱風強度動力研究─邊界層動量與熱交換係數敏感性及superintensity特性

Abstract

颱風強度的動力研究是一個相當廣泛而複雜的問題，即使在今日數值模式與電腦運算高速發展之下，對於颱風強度的模擬仍然存在很大的挑戰。依據靜力平衡、熱力風平衡、對流中性及梯度風平衡等假設的現有理論在颱風內核尺度以及邊界層的問題上不足以充分解釋完整的動力過程，因而在探討颱風強度有其理論的限制。因此本文從理想的三維複雜模式開始，在最簡單的物理架構下，透過機制的討論進一步瞭解颱風強度增強的動力過程，並能解決一部分颱風強度模擬及現有理論詮釋颱風強度所遭遇的困難。 本篇論文的第一部分的主要目標是想檢驗颱風強度與邊界層參數化的關係。在本研究中使用不同邊界層模組時得到的颱風強度演變與結構差異相當大。但選取簡單的邊界層模組，並採用複雜邊界層模組模擬得到的Ck與CD隨風速變化的線性分布後，顯示模式模擬颱風對Ck與CD在高風速下的分布相當敏感，而新的模擬颱風在強度演變與結構皆與原來使用複雜邊界層模組的模擬颱風相似。本研究顯示雖然採取最簡單的邊界層模組，但只要這個邊界層模組可以合理模擬高風速下內流邊界層厚度，並由觀測或更多的理論實驗得到Ck與CD隨風速分布，即使很簡單的邊界層方法也可得到合理的颱風強度模擬。而使用更複雜的邊界層模組，雖然可以更合理詮釋颱風邊界層的發展與模擬，但錯誤估計Ck與CD的情況下，仍會導致不合理的颱風強度發展。複雜邊界層模組的Ck與CD隨風速分布與實際觀測仍有明顯差距，目前實際觀測中的CD隨風速分布雖然可達50 m s-1，但這些觀測資料仍相當有限；而Ck隨風速分布實際觀測資料更只有量到約30 m s-1，因此未來仍需要更多的實驗量測高風速下颱風邊界層的Ck與CD。 在第二部分中本研究詳細比較模式模擬強度與E-PI估計的強度，發現不論是使用bulk-aerodynamic邊界層或是Blackadar邊界層參數化方法模擬的颱風皆為E-PI估計強度的2倍或以上，可視為Persing and Montgomerty (2003)所定義的 superintensity颱風。由其內核結構也可證實颱風的內核具有非常高的相當位溫(θe)分布，由軌跡線分析發現颱風眼內底層的高θe氣塊會輸出額外的能量至眼牆，而這些空氣可由邊界層底部通過眼牆下方的部分內流空氣所置換。 在動力觀點上，颱風內核的增強過程，最大切向風速的增加主要透過絕對渦度產生項。雖然在內流速度最大之處半徑內縮最有效率，但摩擦力仍足以抵銷切向風速的增加，甚至導致次梯度風。考慮絕對角動量守恒且在f平面上，切向風速增加的過程必須伴隨半徑減小，且在半徑越小處越有效率，惟有在半徑夠小之處，絕對角動量內流因半徑減小而使切向風速增加夠快，科氏力矩始有機會大於摩擦力矩而進一步導致超梯度風的形成。 由絕對角動量的分析發現渦旋尺度的增強不一定需要伴隨中層內流，只要在低層有明顯內流即可非常有效率的將外圍高的角動量平流至較小的半徑，透過垂直速度可進一步將低對流層較高的角動量往中高對流層平流，這樣的過程亦可使颱風增強。 總之，本研究在第一個部分中檢驗了三維複雜模式中Ck與CD隨風速的分布對颱風結構及強度演變的敏感度及重要性，並建議需要更多觀測實驗量測高風速下實際大氣Ck與CD隨風速變化，才能進一步降低模擬颱風強度對邊界層的敏感度。在第二個部分中驗證了superintenisty颱風的發生，並利用氣塊軌跡追蹤方法瞭解其形成的機制，發現傳統颱風理論的假設雖然在渦旋尺度的增強及結構分析得到很好的驗證，但在進入颱風內核尺度及邊界層時出現明顯的限制。進一步分析發現颱風眼與眼牆間的交互作用提供颱風的能量循環額外的來源，而邊界層內偏離梯度風平衡的過程亦導致現有的理論失去適用性。

In this paper we examine the simulated tropical cyclone (TC) structure in a full-physics but highly idealized three dimensional model to examine the accuracy of Potential Intensity (E-PI) developed by Emanuel in a three dimensional context. In the first part of the thesis work, we focus on the sensitivities of the simulated TC intensity to the planetary boundary layer (PBL) schemes. Both the equivalent Ck and CD calculated from a more sophisticated PBL scheme, such as the Blackadar and Burk-Thompson PBL schemes, are employed in a modified bulk aerodynamic PBL scheme. The simulated TC intensity and structure strongly resemble those produced by the Blackdar and Burk-Thompson PBL schemes. Based on these works it is suggested that a simple PBL scheme, such as bulk-aerodynamic PBL scheme, with equivalent Ck and CD curves can produce consistent TC intensity with those based on more complicated schemes. This result provides useful physical insights into the vital role of the Ck and CD in determining the TC potential intensity regardless of the detailed representation of the boundary layer parameterization. In the second part of the thesis work, the superintesity behavior as described by Persion and Montgomery (2003) is demonstrated in the simulation with Typhoon intensity exceeding E-PI It is hypothesized that superintensity occurs only with the presence of enhanced low-level eye entropy as indicated by the high equivalent potential temperature in the eye. The high-entropy air is entrained into the eyewall primarily by a breakdown of an azimuthal vortex sheet at the inner edge of the eyewall. It is found that superintensity of a factor of two is shown in both experiments with bulk aerodynamic and with Blackadar PBL schemes. A portion of the low-level inflow moves inward in the PBL under the eyewall and enters the eye, acquiring enhanced entropy through interaction with the ocean beneath the eye. Strong mixing between the low level eye and eyewall below the inversion layer in the eye is identified, fueling the eyewall air with extra entropy from the eye. Meanwhile, the process of inner-core intensification is not in gradient wind balance different from the process of outer region intensification. Supergradient wind is present only in the the region of small radius with large inflow speed, especially in the PBL where the Coriolis force torque exceeds the friction torque. It is shown that the dynamical process based on the gradient wind balance is not valid in the inner-core region.