平行風切流向的非均向化與初始值問題

The Destruction of Isotropy and the Initial-Value Problem of Parallel Shear Flow

林和(Ho Lin)

《大氣科學》 16卷2期 (1988/06) Pp. 117-132

摘要

平行風切流中，對區域集中的擾動之瞬變演化，傳統的特徵分析完全束手無策；其實，Rayleigh方程式中基本機制只有兩項，即不均衡平移與扭轉。均向性因此受到破壞，相位軸可能傾向或垂直於風剖面，但這兩種效應可以經過阿諾限則連結在一起，所以非均向變化必須同時包括這兩項，而且暗示非均向過程可以透過動能，旋能在波譜的傳遞予以解釋。本文將選擇週期性邊界的Sin噴射流作為基本流場，這種風切流本身對擾動而言處於指數型穩定狀態但擾動能量不一定守恆，我們使用解析及數值方法觀察均向渦旋在基本場中逐漸變形的過程。發現非均向平移的效果加諸擾動渦度場如同加諸被動追蹤劑，相位軸順風切傾側，動量通量朝逆梯度方向進行。至於基本場的渦旋梯度項則將相位軸扭往垂直風剖面的方向，擾動旋度通量為順梯度進行，這是風切流不穩定度的來源。我們證明若初始狀態為統計均向，則此時動能、旋能皆處於最低位階，顯而易見，擾動能量將會開始增加，本研究將延伸到WKB解的近似行為上。

關鍵字

均向性 ； 初始問題 ； 平行風切流 ； 連續波譜

並列摘要

The classical eigen analysis of parallel shear flow cannot solve the problem of transcient evolution of a localized perturbation. Yet the basic mechanism of Rayleigh equation consists only two simple effects; the inhomogeneous advection and the bending. The isotropy would be destructed by these two effects but the phase lines can be titled either along or orthogonal to the wind profile. Since the inhomogeneous advection and bending are connected through the Arnold constraint, it is expected that not only a full description of the development of anisotropy has to include both, but also some light can be shed while the evolution being interpretated in terms of the cascade process of eddy energy and enstrophy spectrum.In this study a sine jet with periodic boundary condition was chosen as the basic state. The flow itself is exponentially stable but not necessarily conserving perturbation energy. The deformation of an isotropic vortex was scrutinized by the analytic and numerical methods. We found that inhomogeneous advection, acting on the perturbed vorticity field like on the passive tracer, would tilt the phase lines along the wind shear and henceforth, lead to the up-gradient transport of momentum flux. On the other hand the bending of mean vorticity gradient made the phase lines became perpendicular to the sine profile, a down-gradient transport of vorticity flux proved to be the source of instability.We also showed that the statistically isotropic initial state had the minimum level of energy and enstrophy. Naturally the perturbation energy would start to increase. The further study will focus on the asymptotie behavior of WKB solution.

並列關鍵字

Isotropy ； Initial-value problem ； Parallel shear flow ； Continuous spectrum