The Coriolis force stabilizes pressure systems - Wind speed and vorticity скачать в хорошем качестве

The Coriolis force stabilizes pressure systems - Wind speed and vorticity

This video shows the same simulation as the video    • The Coriolis force stabilizes pressur...   , but with different color gradients. Instead of showing the pressure and wind direction, it shows the wind speed and vorticity. The simulation solves the compressible Euler equations numerically, with an added Coriolis force. This makes the fluid want to turn right compared to its velocity vector, unless a pressure gradient compensates this effect (geostrophic balance). The result is that the pressure systems are more stable, with high pressure systems (anticyclones) turning clockwise, and low pressure systems (cyclones) turning anticlockwise, as it the case in the Earth's northern hemisphere. In the southern hemisphere, the rotations are reversed. The Coriolis force used here is quite large, much larger than in the actual atmosphere, as can be seen from the small circles performed by some particles in zones of intermediate pressure. The video has four parts, showing the same simulation with two different color schemes and at two different speeds: Wind speed: 0:00 Vorticity: 1:44 Wind speed (time lapse): 3:28 Vorticity (time lapse): 4:02 In the first and third part, the color hue shows the speed of the fluid (the norm of the velocity). In the second and fourth part, the color hue shows the vorticity, which measures its quantity of rotation (given by the curl, or rotational, of the velocity field). The velocity field of the fluid is materialized by 1000 tracer particles, whose initial position is distributed randomly over the simulation region. There are periodic boundary conditions. The compressible Euler equations are partial differential equations for the density and the velocity field of the fluid. The system as such is not closed, because the right-hand side of the velocity equation involves the pressure, which has to be linked to known quantities by a thermodynamic relation. I assumed here that the fluid is an ideal gas, so that the pressure is proportional to the density. 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. Render time: 1 hour 34 minutes Color scheme: Parts 1 and 3 - Inferno by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Parts 2 and 4 - Turbo, by Anton Mikhailov https://gist.github.com/mikhailov-wor... Music: Aretes by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/... Source: http://incompetech.com/music/royalty-... Artist: http://incompetech.com/ See also https://images.math.cnrs.fr/Des-ondes... for more explanations (in French) on a few previous simulations of wave equations. The simulation solves the 2D compressible Euler equation by discretization (finite differences). C code: https://github.com/nilsberglund-orlea... https://www.idpoisson.fr/berglund/sof... Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code! #Euler_equation #fluid_dynamics #fluid_mechanics #weather #weather_model #coriolis