Phys. Rev. E 70, 060301(R) (2004) [4 pages]

Mach cone in a shallow granular fluid

Abstract

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Patrick Heil^*, E. C. Rericha^†, Daniel I. Goldman, and Harry L. Swinney^‡
Center for Nonlinear Dynamics and Department of Physics, University of Texas, Austin, Texas 78712, USA

Received 16 July 2004; published 23 December 2004

We study the V-shaped wake (Mach cone) formed by a cylindrical rod moving through a thin, vertically vibrated granular layer. The wake, analogous to a shock (hydraulic jump) in shallow water, appears for rod velocities v_R greater than a critical velocity c. We measure the half angle θ of the wake as a function of v_R and layer depth h. The angle satisfies the Mach relation, sin θ=c∕v_R, where c=√gh, even for h as small as one-particle diameter.

URL:

http://link.aps.org/doi/10.1103/PhysRevE.70.060301

DOI:

10.1103/PhysRevE.70.060301

PACS:

45.70.−n, 47.40.Ki, 41.60.Bq, 47.35.+i

^*Electronic address: Patrick.Heil@urz.uni-heidelberg.de

^†Electronic address: erin@chaos.utexas.edu

^‡Electronic address: swinney@chaos.utexas.edu

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Phys. Rev. E 70, 060301(R) (2004) [4 pages]

Mach cone in a shallow granular fluid