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You are here: Home / Seminars / Colloquium / Exotic Patterns in Faraday Waves

Exotic Patterns in Faraday Waves

Laurette Tuckerman (PMMH, ESPCI)
When Nov 14, 2022
from 11:00 to 12:00
Where Amphi H
Attendees Laurette Tuckerman
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When a fluid layer is vibrated at a sufficiently high amplitude, a pattern of standing waves appears at its surface. Classically, the pattern takes the form of stripes, squares or hexagons, but we also look at more exotic patterns like quasipatterns, heteroclinic orbits, supersquares, and Platonic polyhedra.


A standing wave pattern appears on the free surface of a fluid layer when it is subjected to vertical oscillation of sufficiently high amplitude.  Like Taylor-Couette flow (TC) and Rayleigh-Benard convection (RB), the Faraday instability is one of the archetypical pattern forming systems.  Unlike TC and RB, the wavelength is controlled by the forcing frequency rather than by the fluid depth, making it easy to destabilize multiple wavelengths everywhere simultaneously. Starting in the 1990s, experimental realizations (at ENS-Lyon !) using this technique produced fascinating phenomena such as quasipatterns and superlattices which in turn led to new mathematical theories of pattern formation.   (The first linear stability analysis in viscous fluids also took place at ENS-Lyon.) Another difference is that the Faraday instability has been the subject of surprisingly little numerical study, lagging behind TC and RB by several decades. The first 3D simulation reproduced hexagonal standing waves, which were succeeded by long-time recurrent alternation between quasi-hexagonal and beaded striped patterns, interconnected by spatio-temporal symmetries.  In a large domain, a supersquare is observed in which diagonal subsquares are synchronized.  A liquid drop subjected to an oscillatory radial force comprises a spherical version of the Faraday instability.  Simulations show Platonic solids alternating with their duals while drifting.

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