Incompressible impulsive sloshing

The incompressible impulsive time scale for inviscid liquid sloshing in open rigid containers suddenly put into motion is defined as the intermediate time scale in between the acoustic time scale and the gravitational time scale. Surge and sway boundary-value problems for incompressible impulsive sloshing in some realistic container shapes are solved analytically to the leading order in a small-time expansion. A solution is provided for two types of horizontal cylinders: a triangular cylindrical wedge and a half-filled circular cylinder. The surface velocity and the hydrodynamic force with its corresponding virtual fluid mass are calculated. The cases of constant impulsive velocity and constant impulsive acceleration are linked by transformation equations. Flows with waterline singularities are discussed, being leading-order outer flows in terms of matched asymptotic expansions.