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Mach cone in a shallow granular layer

Patrick Heil·E. C. Rericha·Daniel I. Goldman·Harry L. Swinney
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Abstract

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, theta, of the wake as a function of v_R and layer depth, h. The angle satisfies the Mach relation, sin(theta)=c/v_R, where c=sqrt(gh), even for h as small as one particle diameter.

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Patrick Heil, E. C. Rericha, Daniel I. Goldman, Harry L. Swinney. 2004-09-16. Mach cone in a shallow granular layer. https://doi.org/10.1103/physreve.70.060301

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