A simplistic model for tides - periodic forcing @NilsBerglund

Nils Berglund | A simplistic model for tides - periodic forcing @NilsBerglund | Updated October 2024, 3 hours ago.

$Waves of two different frequencies crossing a randomized square lattice This simulation is similar to the one shown in the video https://youtu.be/pObtx2xmZDA , but instead of being on a regular square lattice, the position of the scatterers has been slightly randomized. The radius of the scatterers is also random. This has a dramatic effect on the waves, which have much more trouble crossing the lattice, a phenomenon related to Anderson localization. The frequency of the lower source is three times the frequency of the upper one. The resulting wavelengths are such that the open intervals in the grating are roughly between both wavelengths. As a result, waves of the lower source pass the grating a bit more easily, as can be best seen on the energy plot. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:27 In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction. There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy). Render time: 34 minutes 25 seconds Compression: crf 23 Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: Where She Walks by Everet Almond See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on a few previous simulations of wave equations. The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf C code: https://github.com/nilsberglund-orleans/YouTube-simulations https://www.idpoisson.fr/berglund/software.html Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #diffraction #grating$

Speed and vorticity of a fluid on a rotating sphere

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Shallow water flowing over an immersed dodecahedron

$Exciting spirals in a circle with sixteen out of phase sources Like several previous videos on this channel , this one shows waves in a circular cavity excited by pulsing sources in other, connected cavities. In this case, there are sixteen sources, pulsing a fraction 1/32 of a period out of phase. The resulting wave patterns start to resemble spirals, as suggested in comments to a previous video. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:27 In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, slightly averaged over a sliding time window. The color dependence on wave height has been chosen quite important, so that the darker regions concentrate near the nodal lines of the waves, that is, the curves where the wave height is zero. Render time: 17 minutes 51 seconds Compression: crf 23 Color scheme: Part 1 - Twilight by Bastian Bechtold https://github.com/bastibe/twilight Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: Asleep by Verified Picasso@verifiedpicasso7260 See also https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations. The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf C code: https://github.com/nilsberglund-orleans/YouTube-simulations https://www.idpoisson.fr/berglund/software.html Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #resonator$

Falling pentagons pretending to be bestagons

The rock-paper-scissors-lizard-Spock equation on the sphere, with improved behavior at the poles