Behavior of Multiple Vortexes of Fluid

Project Title: ‘Numerical Analysis of the Advection and Diffusion of Vorticity with Multiple Vortexes’

Problem Statement: What is the behavior of multiple vortexes of fluid governed by the advection-diffusion shallow water Partial Differential Equations (PDE’s)?

Motivation: Hurricane Sandy was clearly a devastating blow. What would happen if another cyclone was approaching the East Coast simultaneously? Bounce off or merge? Or neither?

Method: We spectrally implement the shallow-water PDE’s assuming periodic boundary conditions and two stretched Gaussians as our initial vorticity.

Results: The following is the behavior of two nearby vortexes. Red represents higher vorticity, or “spinning” velocity.

Conclusions: It appears that the general flow of the fluid is being drawn in between the two vortexes and ejected through the other end. In the case of actual hurricanes, this would cause a magnifier effect of the hurricanes’ strength.