基于边界层理论的分层液膜非线性内波的研究

Study on Nonlinear Internal Waves in the Stratified Liquid Film Based on Boundary Layer Theory

从描述流体流动的Navier-Stokes方程出发,考虑壁面倾斜角度和粘性影响,利用边界层理论对方程进行了简化,再引人流函数变换,经过化简得到带粘性项的Long方程.然后利用摄动法小扰动展开,导出了分层液膜非线性内波的演化方程,最后利用数学软件编程进行了数值求解,得到了在一定密度分布特定条件下的近似解析解.

The fluid flow was described from the Navier-Stokes equations considering the impact of the wall angle and the viscosity. The equations had been simplified by using boundary layer theory, and then introducing the stream function transformation, through the simplification the Long equation with viscous was obtained. Nonlinear internal waves in stratified liquid film evolution equation were derived with the per- turbation method. Finally the approximate analytical solution was obtained in a certain density distribution specific condition by numerical solution of the mathematical software programming.