Explore the fascinating world of Faraday waves in this comprehensive lecture by Laurette Tuckerman from Sorbonne University. Delve into the history, theory, and numerical simulations of the Faraday instability, where standing waves appear on the free surface of a vertically vibrated fluid layer. Discover exotic patterns such as quasipatterns, superlattices, and quasi-hexagons alternating with beaded stripes. Learn about the Benjamin & Ursell inviscid linear stability analysis, viscous stability analysis, and full nonlinear simulations using high-performance computing. Examine the long-time evolution of hexagonal patterns, Fourier spectra, and the intriguing behavior of Faraday super-squares. Investigate the application of these concepts to spherical interfaces and explore predictions from symmetry theory. Gain insights into cutting-edge research on hydrodynamic instabilities and pattern formation in fluid dynamics.
Overview
Syllabus
Date & Time: Thu, 20 February 2020, 11:30 to
Start
The Faraday instability: Floquet analysis, numerical simulation, and exotic patterns
History -- Experiments
Hydrodynamic Instabilities
History -- Theory & Numerics
Benjamin & Ursell inviscid linear stability analysis Linear problem is homogeneous in x,y,
Linear stability problem reduces to:
Result of viscous stability analysis
Exotic Patterns
Two-frequency forcing
Back to single-frequency forcing
Equations and numerical methods
Compare numerical simulation with Floquet analysis Nicolas Perinet
Hexagonal lattice
Computations carried out in minimal hexagonal domain: smallest rectangular domain that can accommodate hexagons
Velocity field at various instants
Hexagonal pattern over one subharmonic oscillation period
Long-time evolution
Stroboscopic films show long-time behavior
Fourier spectra
Fourier spectra : time evolution
Questions: Is this time-dependent behavior in the minimal domain related to the competition between squares and hexagons in a large domain?
High Performance Computing with BLUE
Faraday Super-squares
Experimental study of the Faraday instability
What about a spherical interface subjected to a radical force?
Planar and Spherical
Numerical Floquet analysis
Full nonlinear simulations using BLUE
Predictions from symmetry theory Busse, Golubitsky, Chossat, Matthews, ...
Formulas when patterns are aligned along axis asymmetric
l= 3 tetrahedron
Impossible for pure capillary waves
Taught by
International Centre for Theoretical Sciences
