[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

Abstract

A theory of pebble erosion is presented, based on the assumption that the rate of erosion at a point on the surface is a function Vof the curvature there. It is proved that for physically reasonable functions V,the sphere is the only shape of pebble which can maintain its proportions as it wears away. An argument is given which leads to a particular form for the function Vand a few qualitative consequences of this form are indicated. The surface of the pebble at time tmay be described using spherical polar coordinates θ, Φ by the radius function r (θ, Φ, t). This function is given by a highly nonlinear partial differential equation. However, in the case of the erosion of a deformed sphere, when terms which are of second order or higher in the deformation are neglected, the equation becomes linear and is a version of the diffusion equation. The stability of the spherical shape against deformations of the various harmonic types is then easily analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Dobkins, J. E., and Folk, R. L., 1970, Shape development on Tahiti-Nui: Jour. Sed. Pet., v. 40, p. 1167–1203.

    Google Scholar 

  • Guggenheimer, H. W., 1963, Differential geometry: McGraw-Hill, New York, 378 p.

    Google Scholar 

  • Rayleigh, Lord, 1942, The ultimate shape of pebbles, natural and artificial: Proc. Roy. Soc. Lond., v. A181,p. 107–118.

    Google Scholar 

  • Wardle, K. L., 1965, Differential geometry: Routledge and Kegan Paul, London, 150 p.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bloore, F.J. The shape of pebbles. Mathematical Geology 9, 113–122 (1977). https://doi.org/10.1007/BF02312507

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02312507

Key words

Navigation