Preliminary semi-analytical investigation of momentum exchange in a bouncing container filled with swirling fluid: Pressure impulse induced by central jet

Abstract

This study aims to provide a preliminary semi-analytical description of the momentum reduction in a bouncing cylindrical container filled with swirling fluid upon normal impact with a flat rigid surface, from a hydrodynamic perspective. The focus is on the pressure impulse generated beneath the central jet flow immediately after impact. The fluid motion is modeled using simplified Euler equations with idealized initial conditions and moving boundary conditions. By applying a self-similarity transform, we analytically solve an initial–boundary value problem of the velocity field in a confined target region. This solution allows for a quantitative evaluation of the pressure field. The analysis demonstrates that the rotational motion of the descending flow significantly increases the hydrodynamic pressure near the central axis, thereby exerting a substantial downward stomping pressure impulse on the bottom of the container. This pressure impulse is assumed to be responsible for reducing the momentum of the container, thus also suppressing its bouncing velocity. Based on the analytical results, a semi-analytical method calculating the pressure impulse is proposed, which describes the trend of existing laboratory data.