Below are simulations of an Eulerian level set approach to solve the motion of an incompressible fluid in which the vorticity is concentrated on a lower dimensional set.  Examples include vortex sheets, vortex dipole sheets, and point vortices.   Clicking the image leads to a more comprehensive visualization of the corresponding result.
 

The evolution of the vortex sheet and the velocity field are shown from the side and the top.

The level set function and a vortex are shown.

The level set function and a vortex are shown.

In examples below, two level set functions are used to simulate the motion of point vortices of positive and negative vorticity strengths.  Two level set functions and point vortices are shown.  Point vortices of opposite strengths are depicted in different colors and those of different strengths are shown in different sizes.

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