水體運動對氣-水耦合剪流場穩定性的影響

The Effect of Aqueous Motion on the Instability of Air-Water Coupled flow

郭緯心(Wei-Hsin Kuo)

指導教授 ： 蔡武廷

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202001671

摘要

根據前人解析氣-水耦合流場的研究，定義了兩個不穩定模態—邁爾斯模態 ( Miles mode ) 與漣波模態 ( Rippling mode )，其中的邁爾斯模態為空氣流場主導之不穩定性，漣波模態則是被水體流場所影響，並且在風速值足夠大的條件下才會產生。本研究單純解析水體流場的部分，忽略空氣流場的擾動，目的在於觀察結果是否能夠對照漣波模態的性質。
　　本研究在數值方法上採用契比雪夫多項式 ( Chebyshev polynomials ) 對特徵函數展開，並使用格點配置法來離散計算區間，將控制方程式與邊界條件建構成矩陣形式，進而求解廣義特徵值。
　　計算結果中得到兩種不穩定模態，定義在低風速時出現的為「第一模態」，增大風速後額外出現的為「第二模態」，其中第一模態之角頻率為負值，與邁爾斯模態和漣波模態性質不符合；第二模態與漣波模態有相似的性質，並依據本研究之比較結果證實漣波模態確實為水體流場影響的不穩定性。

關鍵字

線性穩定性分析 ； 自由液面 ； 契比雪夫配置法 ； 剪流 ； 不可壓縮黏性流

並列摘要

According to the stability analysis of air-water coupled flow done by the researchers before, there are two types of unstable mode. The Miles mode results from the air part of the air-water coupled flow, while the rippling mode results from the water part and only occurs at the high wind speed. In this study, we analyze the stability of the water part, and neglects the perturbations of air part. In order to figuring out whether our results can match the rippling mode or not.
　　We apply Chebyshev polynomials to expand the eigenfunction, and the collocation method to discretize the points in the computational domain. We build matrices composed of the governing equation and the boundary conditions, and then solve the problem to get the generalized eigenvalue.
　　The results show two types of unstable modes, and we call the one found at a lower wind speed the “first mode” and the other found when the wind speed increases the “second mode.” The angular velocity of the first modes is negative. This property is different from those of the Miles mode and the rippling mode. Our second mode is similar to the rippling mode, and by the comparison with the studies before, we conclude that the rippling mode is affected by the water part of the air-water coupled flow field.

並列關鍵字

Linear stability analysis ； free surface ； Chebyshev collocation method ； shear flow ； viscous incompressible flow

參考文獻

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