Abstract
A vortex ring in a viscous, incompressible fluid rises obliquely at an angle of 45° toward a deformable free surface. The mathematical description of this flow situation is a time-dependent nonlinear free-surface problem that has been solved numerically for a three-dimensional laminar flow with the aid of the Navier-Stokes equations. Boundary-fitted coordinates were used that include adaptive gridding and grid refinement. For two different Froude numbers at Reynolds number 100, results are presented on the encounter of the vortex ring with the free surface, the deformation of the free surface, the decay of the primary vortices, the generation of surface vorticity and secondary vortices, and reconnection with the free surface. These results are presented in the form of streamlines and equivorticity lines in the plane of symmetry, contour lines of surface elevation, and streamlines and equivorticity lines on the free surface. The two cases reveal a novel ring reconnection at the free surface in the form of a cylindrical sheet.
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