https://doi.org/10.1140/epjp/s13360-021-01634-2
Regular Article
On the ocean beach—why elliptic pebbles do not become spherical
1
I. Physikalisches Institut, Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany
2
Institut Für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany
Received:
25
September
2020
Accepted:
1
June
2021
Published online:
18
June
2021
Among pebbles strewn across a sandy ocean beach, one can find relatively many with a nearly perfect elliptical (ellipsoidal) shape, and one wonders how this shape was attained and whether, during abrasion, the pebbles would remain elliptical or eventually become spherical. Mainly the latter question was addressed in a previous publication which identified frictional sliding and rotation of an elliptic pebble as main abrasion processes in the surf waves. In particular, it was predicted that the ellipticity 
(a > b, principal ellipse axes) converges to a common equilibrium value for elliptic-like pebbles. Unfortunately, the derivation was based on an invalid force expression and a dimensionally unsuitable curvature. In this paper, not only force and curvature but also the contact duration with the sand surface during rotations is taken into account by fairly simple physical arguments, and it is shown that elliptic pebbles neither approach the same ellipticity and nor become more spherical nor more disk-like but rather that the ellipticity 
increases.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
