Mach cone in a shallow granular fluid
Rericha, Erin C.
Goldman, Daniel I.
Swinney, Harry L.
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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 vR greater than a critical velocity c. We measure the half angle u of the wake as a function of vR and layer depth h. The angle satisfies the Mach relation, sin u =c/vR, where c=Îgh, even for h as small as one-particle diameter.