Vortex Dynamics Aspect of the Vortex Interaction

Yesterday, I edited the work of A-dar for NSC annual report. His work is mainly on the laboratory experiments of interaction of two columnar vortex. One of the major contributions of his work is to investigate the vortex system using the vortex dynamic analysis such as the circulation and the total enstrophy. Particularly, the time evolution of the total enstrophy of the vortex system do show a detailed picture of vortex vitality. On the stage of vortex merging, the flow region between those two vortices has a high vorticity gradient which causes a strong decreasing of enstrophy. The insight obtaining from the view of diagnosing the vortex flows by enstrophy is definitely important.

In the good-old-days of the vortex dynamics labs in IAM, we had performed a large number of experiments and had made many efforts on the physics of the interaction between the vortex rings and the boundaries. In these years, we have focusd on the large scale typhoon dynamics and only looked these vortices inviscid and 2-D in the sense of shallow water.

One of my ideas comes this morning is to apply the diagnostic tools of vortex dynamics used in the good old days for further understandings of the typhoon related problems. Some of the potential topics are:

• Binary typhoon interaction, merging, orbiting, and etc.
• Topographic effect; to see what's happened during the interaction.
• Derive the corresponding expression of the enstrophy of the system of vortices with topography within the frameword of shallow water model.

Note that two critical contributions of the time evolution of total enstrophy are made (1) on the boundary for the flux of enstrophy and (2) on the interior for the vorticity gradient.
For example, in the system of binary vortex interaction, the first term may be introduced when the vortex A is strained into the structure of vortex B, i.e., there're input or output of vorticity gradient on the boundary of vortex B. The second term therefore may be looked as the change of vorticity gradient of vortex B during the interaction of these two vortices.

In conclusion, I should pay more attentions on the theorectical aspect and the application aspect of the vortex dynamics analysis in the problem of geophysical vortices dynamics.