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Phase-Locking Parametric Instability Coupling Longitudinal and Transverse Waves on Rivulets in a Hele-Shaw Cell
Grégoire Le Lay1, Adrian Daerr1
1Université Paris Cité, Matière et Systèmes Complexes UMR 7057 CNRS, 75231 Paris cedex 13, France.
Physical Review Letters
|February 6, 2025
Summary
Two damped waves in a fluid system unexpectedly amplified each other, creating a novel convective instability. This discovery in liquid bridges offers new insights into pattern formation and wave interactions.
Area of Science:
- Fluid dynamics
- Wave phenomena
- Nonlinear dynamics
Background:
- Linearly damped waves typically do not lead to instability.
- Coupling distinct wave types can lead to complex emergent behaviors.
- Understanding wave interactions is crucial for controlling pattern formation.
Purpose of the Study:
- To investigate the instability arising from coupling two linearly damped wave types.
- To model and experimentally validate a parametric cross-coupling instability in a liquid bridge.
- To explore the potential for analogous instabilities in other physical systems.
Main Methods:
- Experimental setup involving a liquid bridge between two vertical glass plates.
- Application of external excitation to induce parametric cross-coupling.
- Derivation of a theoretical model using depth-averaged Navier-Stokes equations.
Main Results:
- Observation of a previously unreported convective instability.
- Coherent amplification of coupled longitudinal and transverse waves.
- Experimental confirmation of a synchronization condition selecting a precise wavelength.
Conclusions:
- Parametric cross-coupling of damped waves can generate convective instability.
- The liquid bridge system serves as a model for studying such phenomena.
- Findings suggest potential for similar instabilities in plasma and elastic media.
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