Applet: Sphere rotating in shear flow
When the center of the sphere is fixed, it rotates in a clockwise direction when viewed from the positive $z$-axis, corresponding to a downward pointing curl (green arrow). On the other hand, the vector field is near the sphere is pointing straight in positive $x$ direction. Although the vector field does not appear to be rotating, the change in velocity as one moves perpendicular to the flow still leads to the microscopic circulation captured by curl. Left panel shows the full vector field; right panel shows its projection in the $xy$-plane. To see the rotation of the sphere, hold your mouse cursor over the graph. (If you double-click, the animation will stop; double-click again to restart the animation.)
This vector field is $\dlvf(x,y,z) = (y,0,0)$. One can compute that $\curl \dlvf(x,y,z) = (0,0,-1)$.
Applet files: curl5movedsphere.m, curl5circle2D.m
General information about LiveGraphics3D applets
This applet was created using LiveGraphics3D. To manipulate it, you can
- click and drag to rotate in any direction,
- shift + click and drag up/down to zoom out/in,
- shift + click and drag left/right to rotate around an axis coming out of the screen, and
- press Home to reset to the original view.
Most of the LiveGraphics3D applets have parameters that you can change. In general, you can click and drag points or balls around to change the parameters.
Since these applets use Java, you must have Java installed and properly configured in your browser for the them to display. You can get Java here. If you have trouble getting them to display in your browser, you can visit the LiveGraphics3D troubleshooting page for information on how to get the Java applets to work.
On occasion, even when Java is configured correctly, the Java applets don't load the first time and one instead sees an error message. You can wait a few moments to see if the applet will eventually load itself anyway. You can also reload the page to see if the applet will properly load. Sometimes, one needs to do this multiple times.
