The temporal formation and the shape of ellipsoidal stones on the beaches of the oceans

摘要

On ocean beaches, amongst many irregular shaped stones, a surprisingly large number of stones that are nearly perfect ellipsoids may also be found. The grinding process which forms the ab-plane of the ellipsoid is connected with the rotation around the axis of the greatest moment of inertia (c-axis). A model calculation is presented which shows that a deformed ellipsoid (ovoid) with different curvatures at the a-axis will be finally transformed into the elliptical form by this grinding process. The influence of the density on the shape of the stones is examined by comparing basalt with calcite stones, and interpreted with the rotation around axes with different moments of inertia. Small, but systematic deviations from the ideal elliptical shape are quantitatively measured on a number of stones. The deviations confirm the mechanism that leads to this form: namely, the rotation around the c-axis with slip against the support under the action of the very different vertical accelerations at both the a- and b-axes.