Visualization of 2D turbulence

Relative vorticity in the Euler equations

Taking the curl of the 2D Euler equations yields an equation with relative vorticity as prognostic variable. A numerical model can solve these equations and provides a wonderful insight into the vorticity dynamics in 2D turbulence. In 2014 I used (and older version of) this model

written by Guillaume Roullet to visualize free-decaying 2D turbulence in a biperiodic domain. No forcing is applied and the two videos only differ in their initial conditions. In the first video the initial vorticity is injected on relatively small scales compared to the second video. Shown is actually the sign-conserving 4th root of relative vorticity to highlight more the structures in regions with small values.

One highlight in the video is certainly the appearance of shielded vortices, one can observe also double-shielded vortices and even a few triple-shielded vortices.

Injecting the initial vorticity at larger scales yields a solution that is already much closer to what is expected as final (steady) state: Two stationary vortices of opposite sign spanning the entire domain.