二維對稱性不穩度的數值研究

A Numerical Study of 2D Symmetrically Unstable Convections

許武榮(Wu-Ron Hsu) ； 謝銘恩(Ming-En Hsieh) ； 侯昭平(Jou-Ping Hou)

《大氣科學》 33卷2期 (2005/06) Pp. 103-117

摘要

Solberg、Fjørtoft、Kuo和Eliassen等學者自1930年代起就開始發展對稱性不穩度的理論，然而直到1970、80年代，大家才開始逐漸瞭解對稱性不穩定度在深對流中扮演關鍵角色，而像是鋒生、旋生、颮線甚至層狀降水中，對稱性不穩度受水氣影響，有利對流更進一步發展。雖然對稱性不穩度的理論已相當清楚，但真實大氣環流複雜多變，潛熱和非線性效應使我們無法求得真正的數學解，因此必須使用數值模擬的方式來幫助我們瞭解此問題。
本文使用台大－普度二維非靜力模式(NTU-Purdue 2D nonhydrostatic model)研究對稱性不穩定系統(symmetrically unstable system)。此模式採用顯式的向前向後時間積分格式(explicit forward-backward time integration scheme)，計算高頻波動及內重力波。由於此計算方式極爲穩定，故此模式適合較長時間積分，這對於模擬像傾斜對流這種成長率相當小的個案而言是非常重要的。本次數值計算的結果與傾斜對流的解析解相當吻合，而在模式成功地加入濕動力過程後，考慮潛熱的實驗顯示水氣在調整成長率及對流運動均扮演重要角色。

關鍵字

對稱性不穩度 ； 非靜力數值模式 ； 有效靜力穩定度

並列摘要

Solberg, Fjørtoft, Kuo, and Eliassen developed the theory of symmetric instability in the 50's. It is, however, not until the 70's and 80's people realized its important role in triggering deep convective systems. Interest in moist symmetric instablility has further grown from many perspectives, such as its interaction with frontogenesis, explosive cyclogenesis, and stratiform precipitation associated with squall lines, etc. Although the theory regarding symmetric instability is very clear, the real atmospheric circulation is very complicated. Latent heat, and nonlinear effects make the mathematical solution of the problem difficult, if not impossible. Numerical models are therefore important tools to help us understand the problem.
In this study, the NTU-Purdue nonhydrostatic numerical model is used to study symmetrically unstable systems. In the control dry simulation, our numerical results match the analytical linear solution of a symmetric convection very closely. In the saturated case, the results show that the latent heat effect can drastically alter the length scale, flow pattern, and many aspects of a slantwise convective system.

並列關鍵字

Symmetric instability ； Nonhydrostatic numerical model ； Effective static stability