Vortex Applet

If you have an older Web browser, or a slow internet connection, this applet may take several minutes to load.

There's supposed to be a java applet here. Perhaps Java is disabled?

This applet shows the dynamics of a system of vortices. It is based on a mathematical model which governs the motion of an incompressible fluid. The motion of the vortices is described by a system of ordinary differential equations.

Directions for use

To stop the animation, turn the "Running" checkbox off. To start it up again, turn the "Running" checkbox on.

If the "Drag Vortices" radio button is selected, as it should be when the applet starts, then you can move vortices simply by dragging them with the mouse. It's usually easiest to do this when the animation has stopped, which it does automatically whenever you click on the vortex pane. To start it up again, simply turn the "Running" checkbox back on.

The other two radio buttons allow you to add and remove vortices. If the "Add Vortices" radio button is selected, then clicking on the vortex pane will create a new vortex, which you can then position if you haven't let go of the mouse yet. If the "Remove Vortices" radio button is selected, then clicking on a vortex removes it.

The science behind it

Each circle represents a point vortex, and causes all other vortices to rotate around it in a counterclockwise direction, at a speed which is inversely proportional to the distance between the vortices. This is a simple model, in which all vortices have the same orientation and strength -- a more realistic model would allow for vortices of the opposite (clockwise) orientation and of different strengths.

The numerical method used for simulation is very accurate when the vortices are spaced reasonably far apart, at least one-third the distance between grid points in the vortex pane. When the vortices get closer together than that, the method becomes inaccurate. In particular, it does strange things if vortices are placed right on top of each other. So don't do that.