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Updated: Aug 6, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Forcing function control of Faraday wave instabilities in viscous shallow fluids
Cristián Huepe1, Yu Ding, Paul Umbanhowar
1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208-3125, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
The shape of periodic forcing influences fluid surface waves. Complex forcing functions create harmonic instabilities, while simpler ones lead to subharmonic responses in viscous fluid layers.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Wave Phenomena
Background:
- Parametric forcing of fluid layers can induce surface instabilities.
- The shape of the forcing function's waveform is crucial in determining instability characteristics.
- Resonance tongues describe the parameter space where instabilities occur.
Purpose of the Study:
- To investigate the relationship between forcing function shape and surface wave instabilities.
- To understand how forcing function complexity affects resonance tongue structure.
- To generate and experimentally verify novel harmonic instabilities.
Main Methods:
- Numerical simulations of fluid layer instabilities.
- Experimental measurements of surface patterns.
- Analytical solutions using lubrication theory and WKB approximation.
Main Results:
- Multiple minima in resonance tongue envelopes require forcing functions with >2 extrema per cycle.
- A multi-frequency forcing function generated a distinct harmonic instability.
- Experimental results confirmed transitions between harmonic and subharmonic patterns based on waveform changes.
Conclusions:
- Forcing function shape is a critical factor in controlling fluid surface instabilities.
- Non-sinusoidal forcing can lead to unique harmonic instabilities.
- The study provides a framework for understanding and controlling wave phenomena in fluid layers.
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