The interaction between a counter-rotating vortex pair in vertical ascent and a free surface

Abstract

The inviscid, two-dimensional interaction between a pair of counter-rotating line vortices and a free surface has been studied. A solution to the linearized, small-disturbance problem has been thoroughly explored. For the nonlinear problem numerical calculations were carried out for Froude numbers representing a range of very weak to very strong vortices. Strong vortices are little affected by the presence of the surface, rising to form a bubblelike disturbance; weaker vortices follow paths like vortices approaching a plane boundary. The experimentally observed scarring phenomena—surface depressions whose axes are perpendicular to the flow plane—are seen in the numerical results.