Study On The Generation And Evolution Of The Nonlinear Surface Wave Of Film On Uneven Substrate

The research on the nonlinear wave is widely used in chemical, energy petrochemical industry and it is of great practical and theoretical significance. Currently, many scholars are from the experimental study, numerical calculation and other aspects of a wide range of research and work. Meanwhile, the wave phenomenon of the fluid flow in the uneven bottom surface is also an important heat and mass transfer enhancement techniques, which are also widely used in many industry fields.In this paper, we study an incompressible, viscid fluid with surface tension flow over the uneven bottoms which discussed under the different relationship of the film parameters and topography parameters, and derivate the zero order, first-order and second-order equation of the nonlinear surface wave. And thus the unsteady motion is obtained which considered in the viscosity and surface tension of fluid by different dimensionless, potential flow theory and pseudo-spectral method. At the same time, we treat the unsteady differential equation into the steady differential equation, and thus obtain the approximate analytic of the equation and the expression of the stream function through the coordinate transformation method and other methods.Then, According to the basic principles of pseudo-spectral method, we numerical simulate the solitary wave of a nonlinear equation by the numerical software of Matlab, and draw the wave of the waterfall, so the effects of the generation evolution of the surface solitary which under the different flow state (supercritical state and subcritical state) and uneven wall is discussed. The superimposition feature and the evolutional law of the nonlinear wave on the uneven wall have also been verified.