Numerical simulation of super-square patterns in Faraday waves

TL;DR

This paper presents the first 3D numerical simulations of Faraday wave patterns in large domains, revealing complex superlattice-like structures and pattern formations influenced by container geometry.

Contribution

It introduces a massively parallel hybrid Navier-Stokes simulation approach to study Faraday instability in large 3D domains, uncovering novel superlattice patterns.

Findings

Observation of superlattice-like patterns similar to previous experimental results

Identification of complex patterns including pentagonal cells in cylindrical containers

Patterns are likely widespread in large square containers relative to wavelength

Abstract

We report the first simulations of the Faraday instability using the full three-dimensional Navier-Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid Front-Tracking/Level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in rectangular and cylindrical domains yield complex patterns. In particular, a superlattice-like pattern similar to those of [Douady & Fauve, Europhys. Lett. 6, 221-226 (1988); Douady, J. Fluid Mech. 221, 383-409 (1990)] is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared to the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a square-wave pattern to be accommodated in the center.