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Continuum simulations of shocks and patterns in vertically oscillated granular layers
1Department of Physics, Loyola University Chicago, Chicago, Illinois 60660, USA.
Summary
Collisions between oscillating plates and granular media create shocks. These shocks drive flow reversals, leading to subharmonic pattern oscillations and influencing pattern wavelength.
Area of Science:
- Physics
- Fluid Dynamics
- Materials Science
Background:
- Granular materials exhibit complex behaviors under external forcing.
- Standing waves and shock formation are key phenomena in oscillated granular layers.
Purpose of the Study:
- To investigate the interplay between shocks and standing-wave patterns in granular media.
- To elucidate the role of shock-induced pressure gradients in flow reversal.
- To analyze the relationship between shock strength and pattern wavelength.
Main Methods:
- Three-dimensional, time-dependent numerical simulations.
- Continuum equations solved to Navier-Stokes order.
- Sinusoidal vertical oscillation of a granular layer atop a plate.
Main Results:
- Standing waves form stripe patterns above a critical accelerational amplitude.
- Shocks generated by plate collisions induce pressure gradients.
- These gradients cause flow reversal, resulting in subharmonic pattern oscillations.
- Pattern wavelength increases monotonically with shock strength.
Conclusions:
- Shocks are crucial in driving oscillatory dynamics in granular layers.
- The observed phenomena link shock dynamics to macroscopic pattern formation.
- Frequency and shock strength are key parameters controlling pattern evolution.
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