1. The Generalised Poisson Equation of the vector field with both vorticity and divergence is:
It is shown clearly that the Generalised Poisson Equation recedes to the usual Poisson Equation when the vorticity of the vector fields is zero, that is
2. The Vector Speed Field expressed by the Synthetic Scalar Potential
3. The mathematical model of the cyclone
4. The necessary condition for the existance of the Suction in the Column of Cyclones
5. The vortex-cell linkage of cyclones
The discrete samples of the function are , these samples make a sequence of vortices
Each vortex is called a vortex-cell, they link and superimpose one another. They distribute along a spiral track in the cross-section of the column of a cyclone, as in the figure shown below.
Figure1: The vortex-cell linkage in a spiral track
The mathematical modelling of cyclones has been verified by the practical observation. According to the actual observation, a large tornado, which is a cyclone with suction, often harbours multiple suction vortices inside the column of dust, and subsidiary whirls continually form and dissipate around the bottom edges of a tornado. The spiralling pattern of a ground track left by a tornado shows the highly selective skipping effect that bypass one house and destroy a neighbouring one.