Density and direction of speed of more stable vortices on a rotating sphere

I'm still trying to find good parameter values for vortices in Euler's equations on a rotating sphere to be stable. This simulation features two vortices situated in the northern hemisphere, and rotating in opposite directions. One vortex has a higher density in its center and rotates clockwise, so that it represents a high pressure system. The other vortex rotates counterclockwise and has a lower density in its center, making it a low pressure system. The Coriolis force should help stabilizing the systems, just as it does on the Earth.
The video has four parts, showing the same simulation with two different color gradients and two different representations:
Density, 2D: 0:00
Direction of velocity, 2D: 1:00
Density, 3D: 2:06
Direction of velocity, 3D: 3:06
The 2D parts use an equirectangular projection of the sphere. The velocity field is materialized by 1000 tracer particles that are advected by the flow. In parts 1 and 3, the color hue depends on the density of the fluid, which is related to its pressure, as does the radial coordinate in part 1. In parts 2 and 4, the color depends on the direction of the fluid's velocity, and the radial coordinate depends on its speed. The point of view of the observer is rotating around the polar axis of the sphere at constant latitude. The white bar above the sphere points away from the polar axis in a fixed direction, to indicate the position of points with constant longitude on the sphere.
In a sense, the compressible Euler equations are easier to simulate than the incompressible ones, because one does not have to impose a zero divergence condition on the velocity field. However, they appear to be a bit more unstable numerically, and I had to add a smoothing mechanism to avoid blow-up. This mechanism is equivalent to adding a small viscosity, making the equations effectively a version of the Navier-Stokes equations. The equation is solved by finite differences, where the Laplacian and gradient are computed in spherical coordinates. Some smoothing has been used at the poles, where the Laplacian becomes singular in these coordinates.
Render time: Parts 1 and 2 - 1 hour 2 minutes
Parts 3 and 4 - 1 hour 23 minutes
Compression: crf 23
Color scheme: Parts 1 and 3 - Viridis, by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
github.com/BIDS/colormap
Parts 2 and 4 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Music: "Never Play" by Jeremy Blake@RedMeansRecording
The simulation solves the compressible Euler equation by discretization.
C code: github.com/nilsberglund-orlea...
#Euler_equation #fluid_mechanics #vortex

[@jayantnema9610]

more stable! ☃️☃️☃️

[@gehtsiegarnixan]

looks mesmerizing. Direction would be nicer as a quiverplot though, the colors are hard to read.

[@NilsBerglund]

I was hoping the tracer particles serve that purpose.

[@gehtsiegarnixan]

@@NilsBerglund they do