The Joys Of Volume Visualization

For all of human history we have been trying to find ways to represent a 3D world on 2D surfaces like cave walls, paper, computer screens, etc. So when you simulate some physical process in 3D, it becomes a big challenge to find ways to analyze that data in 3D. The standard way is to either average over one dimension or look at a slice of the volume, but often these are unsatisfying as important features can be wiped out in averages and often don't lie along some coordinate direction that would make it easy to catch in a planar slice of the volume.

Previous answers to this challenge are things like a vanishing point in art. The latest high-tech answer is to use volume visualization software which can use motion to give your brain the impression that what it is viewing is actually three dimensional instead of flat on the screen. For my advanced fluids class this semester, we used volume visualization software called Vapor to preform some of the analysis on a 3D simulation of Kelvin-Helmholtz instability in a stratified flow. For those of you who haven't met KH instabilities before, they occur when you have a strong gradient of velocity in a flow that becomes unstable and leads to turbulent mixing. This process is important everywhere from the oceans to mixing in weather models to accretion disks around black holes. The defining characteristic of KH instabilities are "billows", which can often be seen in clouds like those on the right.

So, to get a feel for this instability, we made some lovely movies of our simulations that allow you to see their 3D nature. Enjoy!

Time evolution of the instability in the y-component of vorticity ( curl(v) ):


Enstrophy ( |curl(v)|^2 ) near the onset of turbulence:


Temperature (hot in red, cold in blue), showing convection in the KH billow: