Controlling Faraday waves with multi-frequency forcing Mary Silber Engineering Sciences & Applied Mathematics Northwestern University http://www.esam.northwestern.edu/~silber Work with Jeff Porter (Univ. Comp. Madrid) & Chad Topaz (UCLA), Cristián Huepe, Yu Ding & Paul Umbanhowar (Northwestern),
37
Embed
Controlling Faraday waves with multi-frequency forcing
Controlling Faraday waves with multi-frequency forcing. Mary Silber Engineering Sciences & Applied Mathematics Northwestern University http://www.esam.northwestern.edu/~silber Work with Jeff Porter (Univ. Comp. Madrid) & Chad Topaz (UCLA), - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Controlling Faraday waves with multi-frequency forcing
Mary SilberEngineering Sciences & Applied Mathematics
Northwestern University
http://www.esam.northwestern.edu/~silber
Work with Jeff Porter (Univ. Comp. Madrid) & Chad Topaz (UCLA),
Cristián Huepe, Yu Ding & Paul Umbanhowar (Northwestern),
Superlattice patternBirfurcation theoretic investigations of superlattice patterns:Dionne and Golubitsky, ZAMP (1992)Dionne, Silber and Skeldon, Nonlinearity (1997)Silber and Proctor, PRL (1998)
Arbell & Fineberg, PRE 2002
FARADAY CRISPATIONS
LINEAR STABILITY ANALYSIS
in modulated gravity
Benjamin and Ursell, Proc. Roy. Soc. Lond. A (1954)
Considered inviscid potential flow:
with free surface given by:
Find satisfy the Mathieu equation:
with gravity-capillary wave dispersion relation
MATHIEU EQUATION
Subharmonic resonance
From: Jordan & Smith
Unique capabilities of the Faraday system
• Huge, easily accessible control parameter space
• Multiple length scales compete (or cooperate) o
vera
ll fo
rcin
g s
tre
ngth
wave number k
(Naïve) Schematic of Neutral Stability Curve:
m/2 n/2 p/2 q/2
cf. Huepe, Ding, Umbanhowar, Silber (2005)
Unique capabilities of the Faraday system• Huge, easily accessible control parameter space
• Multiple length scales compete (or cooperate)
Goal: Determine how forcing function parameters enhance (or inhibit) weakly nonlinear wave interactions.