AN AXISYMMETRICAL FREE-SURFACE WITH A 120-DEGREE ANGLE ALONG A CIRCLE

An axisymmetric flow due to a submerged sink in water of infinite dept h is considered, with a stagnation point on the free surface above the sink. Forbes & Hocking (1990) calculated numerically a flow for each value of the Froude number F smaller than a critical value F-c. For F close to F-c there is a ring-shaped bump on the free surface. At F = F -c, the crest of the bump becomes a ring of stagnation points. We use the numerical procedure of Hocking & Forbes to show that the bump is t he first crest of a train of axisymmetric waves. The wave amplitude de creases with increasing distance from the source. Then we give a local analysis of axisymmetric free-surface flows with a circular ring of s tagnation points. We find flows in which the surface has a discontinui ty in slope with an enclosed angle of 120 degrees all along the ring. This behaviour is consistent with the numerical solution for F = F-c n ear the crest of the bump.