涂布流动的非线性阈值问题

ON THE THRESHOLD PROBLEM OF NONLINEAR STABILITYFOR COATING FLOWS

本文研究了沿斜面流动薄层液体的非线性稳定性,即涂布流动的非线性稳定性问题。我们将周恒对平面Poiseuille流提出的弱非线性理论应用于涂布流动。文中对自由表面的世界条件提出了一个合理的简化方法,对亚临界时不同Reynolds数及扰动频率,求出了有限扰动的阈值。

This paper considers the problem of nonlinear stability of a liquid layer flowing down an inclined plane. A perturbation method, which proposed in the application of weakly nonlinear theory to the problem of stability of plane Poiseuille flow by H. Zhou, is now used here in subcritical range. The simplified boundary conditions are given in this paper.The situations for different Reynolds numbers and wave numbers are calculated. The results indicate that when the Renolds number is near the neutral curve, the subcritical threshold exists. So for coating flows, the finite amplitude disturbance could be unstable when its amplitude is bigger than this threshold.