| Issue |
EPJ Web Conf.
Volume 340, 2025
Powders & Grains 2025 – 10th International Conference on Micromechanics on Granular Media
|
|
|---|---|---|
| Article Number | 03009 | |
| Number of page(s) | 4 | |
| Section | Kinetic Theory and Granular Gas | |
| DOI | https://doi.org/10.1051/epjconf/202534003009 | |
| Published online | 01 December 2025 | |
https://doi.org/10.1051/epjconf/202534003009
Harmonic resonances in granular plane Couette flow
1 Department of Mathematics, Gandhi Institute of Technology and Management, Hyderabad 502329, India
2 Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
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Published online: 1 December 2025
Abstract
The shearbanding instability patterns and bifurcations have been well-studied in granular plane Couette flow using the single-mode Landau equations. However, shearbanding modes interact with each other and undergo harmonic resonances. The present study explores the nonlinear resonant interactions among these shearbanding modes. Using analytical solutions of the linear stability analysis, we determine the critical parameters for harmonic resonance, particularly the 1:2 resonance. At these resonant points, the single-mode Landau equation is invalid because it does not capture the interactions. Thus, a coupled Landau equation is derived to understand 1:2 resonance, where one wavenumber acts as the fundamental harmonic of another. It is found that there is energy exchange between the primary and second-harmonic shear bands, together with amplitude modulation. Thus, harmonic resonance substantially affects macroscopic flow behavior by enhancing or decaying energy dissipation.
© The Authors, published by EDP Sciences, 2025
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