Impact on a floating circular cylinder

The paper deals with the plane unsteady problem of the liquid flow caused by impulsive motion of a semi–submerged circular cylinder, which rests initially on the liquid surface. The liquid is assumed ideal and incompressible and its flow irrotational. The problem is formulated with the help of the Weber variables within the framework of the Lagrangian approach. Third–order initial asymptotics of the solution is built by assuming that the liquid particles on the body surface do not depart from it to become part of the free surface. It is shown that the hydrodynamic pressure is finite in the flow region, but the second–order vertical displacements and the third–order horizontal displacements of the liquid particles are singular at the contact points of the body surface and the free surface. This solution is considered as the 'outer' solution which is valid away from the contact points. In order to take into account the fact the fluid particles on the body surface do depart from it if they are close to the contact points, the 'inner' solution is derived. Positions of the separation points on the cylinder surface are assumed to be prescribed. The 'inner' solution matches the second–order 'outer' solution and describes the shapes of the 'inner' free surfaces which were absent at the instant of impact. It has been revealed that the flow in the spray jet formed by the cylinder impact cannot be properly described by the linear 'inner' solution. Present analysis is focused on peculiarities of the flow generated by the floating cylinder impact, which have to be taken into account in the development of numerical algorithms to tackle impact problems. The theoretical predictions are compared with the numerical results obtained by both the boundary–element method and the finite–difference method. The agreements are fairly good.