Effects of particle sedimentation and rotation on axisymmetric gravity currents

The axisymmetric propagation of a relatively dense gravity current of a given initial volume over a horizontal boundary is considered when the intruding fluid is a suspension of heavy particles and the ambient fluid is steadily rotating about a vertical axis. The investigation employs a shallow-water model of the motion. With the introduction of a strained temporal coordinate, it is possible to derive asymptotic expressions for the evolution of the radius and height of the current, the radial and temporal variation of the horizontal velocity, the volume fraction of particles, and the angular velocity. In this way it is possible to distinguish how the Coriolis force and the effects of particle sedimentation inhibit the radial spreading of the flow. The analytical relationships arise directly from the shallow-water equations and thus improve upon previous simple expressions which are based on an a priori prescription of the shape for the current. The analytical results compare favorably with both numerical integration of the full system of equations and experimental data.(C) 2001 American Institute of Physics.