The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment

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Abstract
The interaction of a vortex ring with a sharp density interface is investigated in the laboratory. Attention is restricted to the case where the Froude number based on the density difference across the interface, the velocity of propagation of the ring normal to the interface and the diameter of the ring is less than unity. It is found that the depth of maximum penetration of the ring, and the diameter of the region of contact between the ring and the interface, are functions of the Froude number. A simple model of the ring-interface interaction which accounts for the observed motion is proposed. This model is then used to calculate the volume rate of entrainment produced by the vortex rings. It is found that this rate of entrainment is proportional to the cube of the Froude number, a result which agrees with measurements of entrainment across density interfaces caused by grid-generated turbulence (Turner 1968) and by a plume incident on the interface (Baines 1973). Thus the vortex ring would appear to be a good approximation to a turbulent eddy in these situations. The main feature of the model is that it identifies the way in which the kinetic energy of the turbulence is converted into potential energy by entraining fluid across the interface. In particular, it indicates that the essential force balance is inertial, and that it is possible to discuss entrainment across a sharp density interface without explicitly invoking either viscosity or molecular diffusion.