本論文研究流體在旋轉圓盤表面上之薄膜流動之弱非線性液動穩定性，探討目標侷限在線性穩定性分析之臨界值鄰近區域。首先利用長波微擾法得到薄膜流體之廣義非線性運動方程式，然後應用正模分析法研究薄膜流體之線性穩定性，並求得線性中立穩定曲線、線性振幅增長率及線性波速。在弱非線性穩定性分析，經由Ginzburg-Landau方程式探討薄膜流體在無條件穩定、亞臨界不穩定、超臨界穩定及超臨界爆炸解等四種臨界狀態存在之必要條件，並從中找出亞臨界區之有限振幅值、超臨界區之平解振幅值及非線性波速。
研究內容主要針對代表旋轉效應之旋轉數及圓盤尺寸大小對不同流體系統穩定性之影響，本文選擇之流體範本分別為牛頓流體、微極流體、磁流體及具有相變化(凝結效應)之流體。茲將研究結果之結論歸納如下：
(一)、旋轉數及圓盤半徑尺寸對於薄膜流體系統穩定性之影響
對於上述四種薄膜流體範本系統而言，經由液動穩定性分析結果得知，旋轉數及圓盤半徑尺寸均具不穩定化效應，此現象之原因為統御方程式中存在之離心力與半徑尺寸相關，增加圓盤半徑尺寸及旋轉數，由於離心力使得線性擾動成長率增加。
(二)、微極參數K對於薄膜微極流體穩定性之影響
對薄膜微極流體而言，微極參數K視為穩定化因子，其原因為微粒旋轉過程中，部份動量喪失，所以渦流黏滯性導致在不同波間進行能量轉移並因而減緩表面波之振幅。
(三)、哈德曼數(m)對於薄膜磁流體系統外加一均勻磁場穩定性之影響
對於薄膜磁流體系統外加一均勻磁場而言，哈德曼數(m)具有穩定化效應，此現象之原因為勞倫茲力(Lorentz force)使得流體速度減緩並制約線性擾動成長率。
(四)、凝結效應對於凝結薄膜流體系統穩定性之影響
與薄膜牛頓流體比較，在相同操作條件下，凝結薄膜流之穩定性較佳，因此具凝結效應能穩定化薄膜流場。

The paper investigates the weakly nonlinear hydrodynamic stability of fluid film flowing on a rotating circular disk. The target is restricted to some neighborhood of critical value in the linear stability analysis. First, a generalized nonlinear kinematic equation is derived by the long-wave perturbation method to represent a film flow. The method of normal mode is applied the linear stability. The neutral stability curve, the linear growth rate of the amplitudes and the linear wave speeds are obtained subsequently as the by-products of linear solution. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various states of the critical flow states, namely sub-critical stability, sub-critical instability, supercritical stability and supercritical explosion in the weakly nonlinear analysis. It is also showed that the necessary conditions of the threshold amplitude and the nonlinear wave speed.
The main object of this paper is to study the effects of rotating parameter, rotation number, and size of circular disk on the stability of the film flow patterns. The chosen fluids are the Newtonian fluid, the micropolar fluid, the magnetic fluid and the film flow with condensation effects.
The conclusions are summarized and drawn as following：
(1)、The effects of rotation number and the radius of circular disk on the stability of the film flow patterns:
In the hydrodynamic stability analysis, hence one can say that rotation number and the radius of circular disk give the same destabilizing effects for the thin flow patterns The reason for this phenomenon is the existence of the centrifugal force term, which is a radius-related force in the governing equation. Increasing the radius and the rotation number results in accelerated growth of the linear disturbance due to the centrifugal force.
(2)、The effect of micropolar parameter K on the stability of a thin micropolar fluid: :
The micropolar parameter K serves as the stabilizing factor for a thin micropolar fluid. The reason is that the part of the momentum is lost in rotating of the particles, so the vortex viscosity will lead to energy transfers between different waves and decay the amplitude of surface waves.
(3)、The effect of Hartman number m on the stability of a thin magnetic fluid under the uniform magnetic field:
Hartman number gives a stabilizing effect for a thin magnetic fluid under the uniform magnetic field. The reason for this phenomenon is the Lorentz forces can modify the velocity field and moderate the growth of the linear disturbance.
(4)、The effect of condensation on the stability of a thin condensate flow :
In comparison with the thin Newtonian fluid, a thin flow with condensation effects is more stable on the same operation condition. It is concluded condensation will stabilize the film flow.

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