Visualization of 3D incompressible flows
Decompose a 3D divergence free velocity field into 3 components:
So that two dimensional divergence of each component vanishes:
Now, for each component define vector potential, which contains only one non-zero component:
Therefore, non-zero components of vector potentials are extensions of two-dimensional stream function: vectors of are tangent to isosurfaces of , respectively.
Visualization of lid-driven flow in a cube
Visualization of natural convection in a laterally heated cube
Conducting horizontal boundaries: Gr=2.9ª106
Animation of slightly supercritical oscillatory flows. Thermally conducting horizontal boundaries, Gr=3ª106.