Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T11:18:37.556Z Has data issue: false hasContentIssue false
  • English
  • Français

The waterlogging of floating objects

Published online by Cambridge University Press:  07 August 2007

DOMINIC VELLA  and
HERBERT E. HUPPERT
DOMINIC VELLA
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
HERBERT E. HUPPERT
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the dynamical processes by which a dense, porous object floating in a body of liquid becomes waterlogged and sinks. We first generalize the classic model of capillary rise in a porous medium to present an analytically tractable model of the process, which is valid for objects that are very shallow compared to their horizontal extent. We find an analytical expression for the time taken for the object to sink under this approximation. We use a series of boundary integral simulations to show that decreasing the horizontal extent of the object decreases the time taken to sink. We find that the results of these numerical simulations are in good quantitative agreement with a series of laboratory experiments. Finally, we discuss the implications of our work for pumice fragments, often found floating in open water after a volcanic eruption, occasionally even supporting plant, animal and human remains.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 245 - 254
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bear, J. 1988 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Bryan, S., Cook, A., Evans, J., Colls, P., Wells, M., Lawrence, M., Jell, J., Greig, A. & Leslie, R. 2004 Pumice rafting and faunal dispersion during 2001–2002 in the southwest pacific: record of a dacitic submarine explosive eruption from Tonga. Earth Planet. Sci. Lett. 227, 135–154.CrossRefGoogle Scholar
Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jerey, D. J. & Knuth, D. E. 1996 On the Lambert W function. Adv. Comput. Math. 5, 329–359.CrossRefGoogle Scholar
Greenhow, M., Vinje, T., Brevig, P. & Taylor, J. 1982 A theoretical and experimental study of the capsize of Salter's duck in extreme waves. J. Fluid Mech. 118, 221–239.CrossRefGoogle Scholar
Jokiel, P. L. 1989 Rafting of reef corals and other organisms at Kwajalein Atoll. Mar. Biol. 101, 483–493.CrossRefGoogle Scholar
Klug, C. & Cashman, K. V. 1996 Permeability development in vesiculating magmas: Implications for fragmentation. Bull. Volcanol. 58, 87–100.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water. I: A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Manville, V., White, J. D. L., Houghton, B. F. & Wilson, C. J. N. 1998 The saturation behaviour of pumice and sedimentological implications. Sediment. Geol. 119, 5–16.CrossRefGoogle Scholar
McBirney, A. R. & Williams, H. 1969 Floating pumice as a means of biological dispersion. Mem. Geol. Soc. Am. 118, 113–116.Google Scholar
Philip, J. R. 1969 Theory of infiltration. Adv. Hydrosci. 5, 215–305.CrossRefGoogle Scholar
Symonds, G. J. 1888 The Eruption of Krakatoa and Subsequent Phenomena, Report of the Krakatoa Committee of the Royal Society. Harrison and Sons.Google Scholar
Thornham, S. A. & Wilson, S. D. R. 1983 The settling of a porous body through a density interface. J. Fluid Mech. 126, 369–378.CrossRefGoogle Scholar
Tsai, W.-T. & Yue, D. K. P. 1996 Computation of nonlinear free-surface flows. Annu. Rev. Fluid Mech. 28, 249–278.CrossRefGoogle Scholar
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273–283.CrossRefGoogle Scholar
Whitham, A. G. & Sparks, R. S. J. 1986 Pumice. Bull. Volcanol. 48, 209–223.CrossRefGoogle Scholar