An accurate model for the thin film flow

This paper deals with the linear stability of a liquid film flowing down an inclined plane. The Navier-Stokes equations were reduced into four evolution equations that describe the development of the film depth, the flow rate, the free surface velocity, and the wall shear stress, using the Karman-Polhausen boundary layer integral method. Thus, we were able to determine the stability threshold and approach well the critical wave number for long waves. The obtained results were found to be in good agreement with the experiments of Liu et al.

On the refracted patterns produced by liquid vortices

A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex＇s free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.

Particle Paths of Lagrangian Velocity Distribution Simulating the Spiral Arms of Galaxy M51

星系是恒星的巨大的家庭由他们的自己的严肃保持完整。系统 M51 是一个螺线星系。它拥有十亿颗星。螺线手臂的范围扩大 10 万光年。现在的学习在在使用 Lagrangian 流动领域的粒子路径模仿星系 M51 的螺线手臂的一次尝试。Lagrangian 流动地被介绍。在在二同心柱体之间的空间的液体粒子的起始的地点首先被指定。然后，液体粒子的线速度分布与粒子的不同角度旋转被使用在 Lagrangian 图获得粒子路径。为模仿星系 M51 的螺线手臂， Lagrangian M51 图被开发。Lagrangian M51 图的粒子路径与星系 M51 的螺线手臂同意相当好。