Journal of Fluid Mechanics

Papers

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

RAYMOND BERGMANNa1 p1, DEVARAJ VAN DER MEERa1 c1, STEPHAN GEKLEa1, ARJAN VAN DER BOSa1 and DETLEF LOHSEa1

a1 Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands

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 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 xs221D Fr1/2 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 Vbubble of air entrained by the process, namely, Vbubble/h03xs221D(1 + 0.26Fr1/2)Fr1/2.

(Received March 31 2008)

(Revised February 20 2009)

Correspondence:

c1 Email address for correspondence: d.vandermeer@utwente.nl

p1 Present address: Department of Physics and Centre for Fluid Dynamics, The Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark

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