一类新的不可压缩旋涡流动精确解

A new class of exact solutionof incompressible vortex flow

流体力学基本方程的精确解是一个重要的研究方向,精确解对于流动物理机理的认识具有不可替代的作用,并且对数值模拟方法的发展具有可比较性.利用多项式完全判别系统法,对仅具有径向流动的三维不可压缩旋涡流动问题进行研究,给出了该方程基于多项式判别系统法的所有精确解分类,得到了七类新形式的具有径向流动的不可压缩旋涡流动精确.这一新的解法主要优点在于能确定解分类的参数区域,并且具有数学上的完备性质,这是目前其他相关研究无法得到的结论,并具备实际物理问题应用的潜在价值.

The exact solution of the fundamental equations in fluid mechanics is an important research direction. The exact solution plays an irreplaceable role for the physical mechanism understanding, as well as for the development of numerical simulation method. One of the most celebrated exact solutions of the Navier-Stokes equations is associated with the flow which has only the radial velocity component. The problem was first studied by many researchers. However, more comprehensive treatments have been given in this paper. In what follows we adopt the approach of the concept of polynomial complete discrimination system, and new seven kinds of solution are obtained. This new method of main advantage is to determine the solution parameter region classification, and has the complete nature of mathematics, which is the other related research is unable to obtain the conclusion, and has potential value of application of the actual physical problems.