A note on impulsive sphere motion beneath a free-surface

A general framework is presented for solving the impulsive oblique motion o f a spherical body in close proximity and below a free-surface, The fluid i s considered to be impulsive and the flow as incompressible. The irrotation al flow field is deduced from a velocity potential. The full nonlinear prob lem is reduced to a sequence of boundary-value problems by employing a smal l-time expansion technique. The mixed boundary conditions are of a Dirichle t type on the undisturbed free-surface and of a Neumann type on the equilib rium spherical shape. The solution is obtained by employing a Green's funct ion and the method of multipoles expansions. General expressions. correct t o each order in the small-time, are given for the free-surface deflections and the pressure force experienced by the moving sphere.