Resonant Interactions, MultiFrequency Forcing, and Faraday Wave Pattern Control
Abstract
Standing surface waves form on a layer of fluid when it is subjected to a sufficiently strong periodic acceleration in the vertical direction. There have been numerous theoretical and experimental investigations of pattern formation in this socalled Faraday wave system in the last 15 years or so, in part because it exhibits patterns not seen in other systems (rhombic and triangular patterns, quasipatterns, superlattice patterns, localized structures akin to oscillons, etc.). Hence it provides a versatile framework in which to develop and test our general understanding of the nonlinear pattern formation process in hydrodynamic systems. However, this versatility comes at some cost. Specifically, many of the more exotic patterns are only realized when the periodic forcing function contains more than one frequency component; the introduction of nonsinusoidal periodic forcing functions leads to a large control parameter space that is difficult to fully characterize. For example, there is an increase from 2 parameters (frequency and amplitude) to 5 parameters in the next simplest case of twofrequency forcing (frequencies, amplitudes and relative phase). We report on research that helps explain the role of each of the forcing function parameters in the pattern formation process. We focus on resonant triad interactions and their contribution to the weakly nonlinear pattern formation process for twofrequency forced parametrically excited surface waves.
 Publication:

Sixth Microgravity Fluid Physics and Transport Phenomena Conference: Exposition Topical Areas 16, vol. 2
 Pub Date:
 November 2002
 Bibcode:
 2002mfpt....2..582S
 Keywords:

 Surface Waves;
 Resonant Frequencies;
 Nonlinearity;
 Standing Waves;
 Faraday Effect;
 Control Theory;
 Periodic Functions;
 Polarization (Waves);
 Excitation;
 Superlattices;
 Scaling Laws;
 Frequency Distribution;
 Fluid Mechanics and Thermodynamics