A linearized model of water exit

Abstract

A model of hydrodynamic loads acting on a rigid floating body during the lifting of the body from the liquid surface is presented. The liquid is of infinite depth, inviscid and incompressible. Initially the liquid is at rest. The body suddenly starts to move upwards from the liquid at a constant acceleration. Boundary conditions on the liquid surface are linearized and imposed on the equilibrium position of the liquid surface. The resulting boundary problem is solved by the methods of analytical functions. Negative pressures are allowed and the pressure is assumed continuous at the periphery of the wetted area. The unknown size of the wetted area is determined by the condition that the speed of the contact points is proportional to the local velocity of the flow. This condition provides a nonlinear Abel-type integral equation which is solved explicitly. Both two-dimensional and axisymmetric configurations are considered. Predicted hydrodynamic forces are compared with the computational fluid dynamics results by Piro & Maki (<jats:italic>11th International Conference on Fast Sea Transport. Honolulu, Hawaii, USA</jats:italic>, 2011) for both a rigid wedge and circular cylinder, which initially enter the water and then exit from it.