Abstract
The initial motion of a pair of strong vortices suddenly created close to a free surface is calculated analytically by means of a Taylor expansion in time. While weak vortices moving toward a free surface repel each other [see Hydrodynamics (Cambridge U.P., Cambridge, 1932)], strong vortices attract each other to the leading order. But, they cannot merge and annihilate each other because of nonlinear free-surface effects. Several features of the solution depend on whether or not the vortices are below a critical depth. At the critical depth the two vortex points span an angle of 120° with respect to the surface center. The dominating gravitational effects are investigated.
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