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Physical Review Letters

Volumn 72, Issue 1, 1994, Pages 172-175

Transition to parametric wave patterns in a vertically oscillated granular layer

(3) Melo, Francisco a Umbanhowar, Paul a Swinney, Harry L a

a UNIVERSITY OF TEXAS AT AUSTIN (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010312352 PISSN: 00319007 EISSN: None Source Type: Journal
DOI: 10.1103/PhysRevLett.72.172 Document Type: Article

Times cited : (334)

References (21)

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- Parametric granular waves have been previously observed in a one-dimensional configuration (a narrow channel);

14
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- the periodicity of these waves was mainly imposed by boundary conditions, while in our case the wave number appears to be intrinsic.

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18
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- A rough estimate of δ t is δ H /Vc, where Vc is the impact velocity and δ H the maximum dilation of the layer. Assuming that Vcapprox 2 π f A, we have δ t approx 2 π f δ H / Γ g. Thus the spreading of the collision time is negligible when Γ g / 2 π f2δ H >> 1 (δ t << 1/f). We have little insight about δ H; it is an increasing function of H and a slowly varying function of A.

19
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- Particles in contact with the bottom of the container cannot lose contact first because, in that case, an air flow would be needed to fill the gap left by the relative motion of the layer. The motion of particles close to the free surface does not require such a flow.

20
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- See, for instance, L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1984), p. 36.

21
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- This interpretation suggests that parametrically excited granular waves should disappear in materials with a very low coefficient of restitution.

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