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

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h(0) 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 giving excellent agreement. 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 the contraction phases of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly as 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 and the scaling of the volume V-bubble of air entrained by the process, namely, V-bubble/h(0)(3) proportional to (1 + 0.26Fr(1/2))Fr-1/2.