SOME OPINION FOR CONSIDERING FRICTIONAL TERM AND SMOOTHING PROCESS IN THE BAROTROPIC VORTICITY EQUATION

First of all, this paper discusses how to choose smoothing coefficient in accordance with the grid size of space. Secondly we study the influence on the solution of the differential equation by adding frictional term in the vorticity equation, and then show how to choose suitable frictional coefficient in this case. Thirdly we discuss the influence for computational stability of the finite difference scheme after adding frictional term in the vorticity equation. It is shown that the computation is stable, if taking the frictional term in the(n-1) time layer in the normal centered time difference scheme. If taking the frictional term in the n time layer, then the computation of the difference scheme is unstable. At the same time, the time forward difference scheme may be stable also after adding frictional term, but the frictional coefficient required is then much larger. Finally, we discuss the relation between the smoothing process and frictional term for numerical prediction using the vorticity equation. From the viewpoint of computation, the two things are not equivalent. But we might determine suitable smoothing coefficient by comparing the smoothing process in a diffusion equation.