Decaying two-dimensional turbulence

We solve the two-dimensional incompressible Euler equations using a vorticity–streamfunction formulation.

``````#include "grid/multigrid.h"
#include "navier-stokes/stream.h"
``````

The domain is square of size unity by default. The resolution is constant at ${256}^{2}$.

``````int main() {
init_grid (256);
run();
}``````

The initial condition for vorticity is just a white noise in the range $\left[-1:1\right]$ .

``````event init (i = 0) {
foreach()
ω[] = noise();
}``````

We generate images of the vorticity field every 4 timesteps up to $t=1000$. We fix the colorscale to $\left[-0.3:0.3\right]$.

Evolution of the vorticity

``````event output (i += 4; t <= 1000) {
output_ppm (ω, min = -0.3, max = 0.3, file = "omega.mp4");
}``````