Math Insight

Applet: Fluid flow through oriented helicoid

Applet: Fluid flow through oriented helicoid

Applet loading

Applet: Fluid flow through oriented helicoid -- subpapplet

Applet loading

The function $\dlsp(\spfv,\spsv) = (\spfv\cos \spsv, \spfv\sin \spsv, \spsv)$ parametrizes a helicoid when $(\spfv,\spsv) \in \dlr$, where $\dlr$ is the rectangle $[0,1] \times [0, 2\pi]$ shown in the first panel. The cyan vector at the blue point $\dlsp(\spfv,\spsv)$ is the upward pointing unit normal vector at that point. The magenta vector field represents fluid flow that passes through the surface. In this example, the vector field is the constant $\dlvf=(0,1,1)$. You can drag the blue point in $\dlr$ or on the helicoid to specify both $\spfv$ and $\spsv$.

Applet links

This applet is found in the pages

List of all applets

Notation systems


More information on notation systems

General information about three.js applets

The applet was made using three.js and requires Javascript as well as a browser that supports WebGL. For most three.js applets, you can drag with the mouse to rotate the view, drag with the right button to pan, and zoom in/out with the mouse wheel. Many applets contain points that you can drag to change values of variables.