對von Kármán旋轉流的進一步研究

Abstract

我們比較了von Kármán方程式的數值解與線性近似的結果,發現某些von Kármán方程式的解的特性,能夠被其線性化方程所表現。為了更進一步驗證這個結果,我們採用amplitude equation。為了解決 damping 項造成的影響,我們提出一個新的方法。此方法雖然amplitude部份近似的很好,但phase部份相當差,有待進一步的研究。

By the comparison between the numerical results and the linearized solution,we show some solutions of von Kármán’s equation have global feature that can becaptured by the linearized solutions, although there are some shifts in amplitudeand phase. To show the validity of this approach and polish the approximation, we use the amplitude equation approach, which can tune the amplitude and phase of the linearized solutions to make them fit. We encounter difficulty in the course of finding the amplitude equation of damping systems. To solve this problem, we propose an idea to deal with the exponential growth of the zero-th order solution. Although the phase of the approximate solution deviates from the numerical results very much, the amplitude fits well. Further investigation is under way.