frozen_waves.md

«Frozen waves» at the interface between non-miscible fluids with strong density contrast
- References

«Frozen waves» at the interface between non-miscible fluids with strong density contrast

This folder contains the code used to simulate frozen waves between non-miscible fluids with strong density contrast, from Gréa et al. (2025). The main objective was to reproduce / complement the experimental observations carried at the CEA-CESTA facility, which aimed at measuring centimeter-scale “frozen waves” well inside the unstable region, where the interface is expected to grow with the square of the forcing velocity.

An example of the experimental observations is shown in the figure below.

An example of «frozen waves» measured at the interface between LST Heavy Fluid and Silicone Oil subject to horizontal vibrations with velocity amplitude of 0.5 m/s and frequency of 200 Hz taken from Gréa et al. (2025).

Code is divided in two parts:

Simulations with walls aimed at reproducing the experimental setup: with_walls/main.c
Simulations without walls aimed at studying the instability in an infinite domain: without_walls/main.c

This approach allowed to show the role of confinement on the instability growth and isolate the sidewall effects, which are a separate phenomenon from the instability itself.

An example of the results obtained using Basilisk using the same setup as in the experiment, a forcing frequency of 200 Hz and different forcing velocity amplitudes ranging from (a) 0.125 to (e) 0.625 m/s. This sequence illustrates the boundary effects, then, the formation of frozen waves near the center of the domain, and gradually the secondary instability, which encourages fragmentation. A similar sequence was observed in the experiments. — An example of the results obtained using `Basilisk` using the same setup as in the experiment, a forcing frequency of 200 Hz and different forcing velocity amplitudes ranging from (a) 0.125 to (e) 0.625 m/s. This sequence illustrates the boundary effects, then, the formation of frozen waves near the center of the domain, and gradually the secondary instability, which encourages fragmentation. A similar sequence was observed in the experiments.

References

[grea:2025]

Benoit-Joseph Gréa, Andrés Castillo-Castellanos, Antoine Briard, Alexis Banvillet, Nicolas Lion, Catherine Canac, Kevin Dagrau, and Pauline Duhalde. Frozen waves in the inertial regime. Journal of Fluid Mechanics, 1021:A12, 2025. [ DOI | http | .pdf ]