Numerical study of the material transport in the viscous vortex dipole flow

Abstract

This paper presents a numerical study of the material transport of Lamb dipole(s) in the two-dimensional viscous flow. We focus on the properties of the rate of strain tensor, which has received less attention in the literature. It is noted that the eigenpairs of the tensor explicitly indicate the strength and direction of material stretching and compressing. The tensor provides a clear map of the material motion regardless of the complexity of the vortical flow. The strain rate field displays a rich structure as it contains five elliptic points and six hyperbolic points. It is interesting to observe that the left elliptic point of the strain rate field bifurcates into two at t > 0. Two kinds of material curves, circular and vertical, are used to illustrate the flow transport. The transport mechanism discussed here can be employed to explore the transport in more complex vortex flows.