Interactions of three viscous point vortices

초록

The dynamics of viscous point vortices in two dimensions is studied both analytically and numerically. We consider a core-growth model based on the Lamb-Oseen vortices, the so-called multi-Gaussian model, to describe the evolution of viscous vortices. We focus mainly on the interaction of three viscous vortices. It is found that for three vortices, there are no self-similar motion except rigid rotation, and no collapse of the vortex centers, unlike the inviscid point vortices. We perform numerical computations for the Navier-Stokes equation and the multi-Gaussian model for the collapsing case of the inviscid three point vortices and examine in detail the viscous evolutions of the vortices from the models. The motions of the vortices are little influenced by viscosity, when their mutual distances are fairly large, but the dynamics is altered by viscosity as the vortices get close to each other and the cores of the vortices overlap. The multi-Gaussian model demonstrates the prevention of the total collapse of the vortices by the viscosity effect, and the merging process of two vortices, which are the main qualitative features of the Navier-Stokes solutions.

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