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Mach cone in a shallow granular fluid.

Patrick Heil1, E C Rericha, Daniel I Goldman

  • 1Center for Nonlinear Dynamics and Department of Physics, University of Texas, Austin, Texas 78712, USA. Patrick.Heil@urz.uni-heidelberg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
Summary

A V-shaped wake forms behind a moving rod in a vibrated granular layer. This granular wake, like a hydraulic jump, follows the Mach relation, even for shallow layers.

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Area of Science:

  • Granular physics
  • Fluid dynamics
  • Nonlinear phenomena

Background:

  • Granular materials exhibit complex behaviors when subjected to external forces.
  • The formation of wakes and shock-like structures in granular media is analogous to phenomena in fluid dynamics, such as hydraulic jumps.

Purpose of the Study:

  • To investigate the V-shaped wake (Mach cone) generated by a cylindrical rod moving through a vertically vibrated granular layer.
  • To determine the critical velocity for wake formation and analyze the wake's half-angle dependence on rod velocity and layer depth.

Main Methods:

  • Experimental setup involving a cylindrical rod moving through a thin, vertically vibrated granular layer.
  • Measurement of the wake's half-angle (theta) as a function of rod velocity (vR) and granular layer depth (h).

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Main Results:

  • A V-shaped wake is observed for rod velocities exceeding a critical velocity (c).
  • The wake's half-angle (theta) follows the Mach relation, sin(theta) = c/vR.
  • This relationship holds true even for granular layer depths as small as one particle diameter.

Conclusions:

  • The study demonstrates that a Mach cone, analogous to a hydraulic jump, forms in vibrated granular media.
  • The critical velocity (c) is related to the granular layer depth (h) by c = sqrt(gh), consistent with shallow water theory.
  • These findings highlight the applicability of fluid dynamics principles to granular systems.