On the ocean beach -- why elliptic pebbles do not become spherical

TL;DR

This paper investigates why elliptic pebbles on beaches do not become spherical during abrasion, correcting previous models by including contact duration and showing ellipticity tends to increase rather than decrease.

Contribution

It introduces a revised physical model accounting for contact duration, demonstrating that elliptic pebbles do not become spherical but tend to become more elliptical.

Findings

Elliptic pebbles' ellipticity increases over time.

Previous models incorrectly predicted convergence to a common shape.

Inclusion of contact duration alters abrasion outcome predictions.

Abstract

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 $\epsilon$ 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 $\epsilon$ increases.