Point Vortex Dynamics

These models find the motion of a set of point vortices. Associated with each vortex is a flow which moves the others around. The flow decays as 1/r away from the vortex. The dynamics can be represented as a Hamiltonian system:

Equations here---

Begin:

To begin, click on to download the main software pieces and start up your matlab process.

Initial conditions:

Specify the initial positions and strengths of the vortices as a N-by-3 matrix vort (either explicit or defined using functions) where the columns give the x,y,strength values and the rows separate the data for each vortex. E.g.

vort=[1.01,0,1; 0,1,1; -1,0,1; 0,-1,1];

or

th=[0:9]'*pi/5;vort=[cos(th),sin(th),ones(10,1)];vort(1,1)=vort(1,1)+0.1;

Initial data:

Numerical:

Domain for plot (xmin,xmax,ymin,ymax):

Time step:

Time between between displays:

Maximum time:

When you click the screen will show the initial conditions and the velocities (excluding the self-induced velocities near the vortices themselves). Click on the screen and the movement will begin.

Continue

Plot distance from the origin of the first vortex vs time

Shear:

You can also include a background shear flow U = s*y. Try values such as s = -0.5 with the 8 vortex model...

Shear:

Click Here to view the Matlab code directly. You can save it and run stand-alone.