Constructions of some exact vortex superposition solutions

In theoretical ways to solve the N-S equation, we will confront many difficulties. For example, the complex mathematical calculation, the 3D velocity components and the nonlinear terms, etc. We find that from the basis of Stokes-Helmholtz decomposition and after some processing, we can get a method of constructing the vortex superposition solutions. We get a set of exact solutions in different coordinates and we hope these solutions will be helpful to a clearer understanding of the vortex in Fluid Mechanics.