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Updated: Jul 16, 2026
10:35
Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Band gaps and the Kelvin-Helmholtz instability
1Department of Biomathematics and Department of Mathematics, UCLA, Los Angeles, California 90095-1766, USA.
Summary
We studied fluid instability with a flexible plate. Periodic plate rigidity generally destabilizes flow, but specific wavelengths can be stabilized or further destabilized due to Bragg reflection effects.
Area of Science:
- Fluid dynamics
- Instability analysis
- Solid mechanics
Background:
- The Kelvin-Helmholtz instability is a fundamental phenomenon in fluid dynamics.
- Flexible interfaces can significantly alter fluid flow stability.
- Periodic material properties introduce complex boundary conditions.
Purpose of the Study:
- To analyze the linear stability of two inviscid fluids separated by a flexible plate under shear.
- To investigate the impact of spatially periodic flexural rigidity on flow stability.
- To determine conditions for enhanced destabilization and stabilization due to plate periodicity.
Main Methods:
- Linear stability analysis of inviscid, sheared fluids.
- Application of Bloch's theorem (Floquet theory) for periodic systems.
- Derivation of a non-Hermitian matrix to compute eigenvalues and the dispersion relation.
Main Results:
- Identified conditions for exponential growth of velocity perturbations based on plate rigidity and shear rate.
- Demonstrated that plate periodicity generally destabilizes the flow compared to uniform plates.
- Observed enhanced destabilization and stabilization for specific disturbance wavelengths near multiples of the plate periodicity.
Conclusions:
- Spatially periodic flexural rigidity significantly impacts fluid flow stability.
- The interaction between Bragg-reflected modes and plate periodicity is crucial for understanding stability.
- This work provides insights into controlling fluid instabilities using patterned interfaces.
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