论文标题
2D稳定的Navier-Stokes方程的一般解决方案，用于不可压缩的流量而没有涡旋扩散
General Solution to 2D Steady Navier-Stokes Equation for Incompressible Flow without vorticity diffusion
论文作者
论文摘要
该研究求解了通用解决方案，用于2D稳定的Navier-Stokes方程，以使其不可压缩的流量无涡流扩散，这比Stokes流动更一般。为了获得一般解决方案，引入了两个电势函数以表达速度：描述旋转不可压缩流的矢量电位和描述不可压缩流动流的标量电势。结果表明，用电势函数表达的涡度方程是双旋函数的函数，这意味着描述流场的电势函数是多项式不超过四度的多项式。对于稳定的单向剪切流，可以用第三度多项式表达的矢量电势来描述速度和压力场。对于非单向二维稳定剪切流，这两个电势函数中可能有四个独立参数。
The study solves the general solution to 2D steady Navier-Stokes equation for incompressible flow without vorticity diffusion, which is more general than Stokes flow. In order to obtain the general solution, two potential functions are introduced to express the velocity: a vector potential describing the rotational incompressible flow and a scalar potential describing the irrotational incompressible flow. The results show that the vorticity equation expressed with potential functions is a biharmonic function, which means that the potential functions describing the flow field are polynomials of no more than fourth degree. For a steady unidirectional shear flow, the velocity and pressure fields can be described with the vector potential expressed by a polynomial of third degree. For non unidirectional two-dimensional steady shear flow, there may be four independent parameters in the two potential functions.
