Controlled impact of a disk on a water surface: Cavity dynamics

TL;DR

This study investigates the cavity dynamics caused by a disk impacting water at various Froude numbers, combining experiments, simulations, and a simple model to understand the cavity's behavior and scaling laws.

Contribution

It introduces a simple radial cavity model that captures asymmetry, scaling laws, and air entrainment during disk impact on water surfaces.

Findings

Excellent agreement between experiments and simulations.

Cavity depth scales roughly as Fr^{1/2}.

Air bubble volume scales with Fr^{1/2} and asymmetry insights.

Abstract

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high speed imaging and compared to boundary integral simulations. An excellent agreement is found between both. The flow surrounding the cavity is measured with high speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations. We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and contraction phase of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly proportional to Fr^{1/2} with a weakly Froude number dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity, the scaling of the volume Vbubble of air entrained by the process, namely Vbubble/h0^3 proportional (1 + 0.26Fr^{1/2})Fr^{1/2}, and gives insight into the axial asymmetry of the pinch-off process.