关于不可压缩黏性流中边界涡量产生的物理机制

On physics of boundary vorticity creation in incompressible viscous flow

本文围绕不可压缩流动中边界涡量产生这一有争议的话题展开讨论,指出边界涡量产生必须是一个有黏过程,并从宏观和介观角度系统地反驳了无黏论.黏性不仅参与边界涡量的扩散,而且在它的产生过程中起到了实现无滑移边界条件的作用.Lyman涡量流可看作是Lighthill-Panton-Wu边界涡量流的一部分,提供了边界涡量动力学的一种可选择解释.与现存的无黏边界涡量产生观点不同,我们认为黏性对Lyman涡量流的产生是必不可少的.表面压力分布的形成是无黏过程,而压力梯度产生边界涡量流则是一个有黏过程,这两个基本过程的时间间隔与分子弛豫时间同量级.本文进一步提出从Boltzmann方程的角度来阐明黏度的关键角色以及各种相关物理概念之间的内在联系.对于无滑移边界下的连续流,无黏欧拉理论中滑移速度的物理载体是边界物质涡层中的涡量.有趣的是,本文指出Lyman涡量流也适用于滑移流模式,其黏性机理隐含在有非连续流效应的Knudsen层中.因此,一个包含边界涡量产生和机翼环量形成的完整物理图像必须建立在有黏流动的基础之上.

The present paper provides some arguments surrounding the controversies of boundary vorticity creation for incompressible viscous flow.Our discussion shows that boundary vorticity creation must be a viscous physical process.Importantly,it is emphasized that not only viscosity is responsible for spreading the generated vorticity out of the boundary,but also must be involved in the process of boundary vorticity creation to realize the no-slip boundary condition.Lyman flux is a part of the boundary vorticity flux under the Lighthill-Panton-Wu’s definition,which provides an alternative interpretation of boundary vorticity dynamics.Different from the existing inviscid interpretation,we insist that viscosity is fully indispensable for generating the Lyman flux through the tangential boundary acceleration and surface pressure gradient where the acceleration adherence is shown to be derived from the velocity adherence directly.Through a detailed discussion on interfacial vortex sheet and slip velocity,it is revealed that the velocity jump across the material interfacial vortex sheet(a thin viscous shear layer as the fluid viscosity approaches to zero)is physically different from that across the interface.In addition,it is shown that the formation of surface pressure distribution is an inviscid process while the subsequent boundary vorticity generation by the tangential pressure gradient must be a viscid process(contributed by the non-equilibrium particle relaxation effect).These two processes are separated by a non-zero time increment with the same order as the particle relaxation time.Then,the hydrodynamic limit of the Boltzmann equation is revisited to elaborate the crucial roles of viscosity for both the continuum and slip regimes.For continuum flows with a no-slip boundary,the physical carrier of the slip velocity in the inviscid Euler theory originates from the produced vorticity concentrated in the thin material vortex sheet.Interestingly,we find that Lyman flux must be a viscous boundary flux even for a slip boundary where the implicit viscid mechanism is attributed to the non-continuum effect hidden in the Knudsen layer.The present exploration suggests that a complete physical picture including the boundary vorticity creation and the formation of airfoil circulation should be built upon the viscous flow theory.