Shape evolution of ooids: A geometric model

Abstract

Striking shapes in nature have been documented to result from chemical precipitation - such as terraced hot springs and stromatolites - which often proceeds via surface-normal growth. Another studied class of objects is those whose shape evolves by physical abrasion -The primary example being river and beach pebbles - which results in shape-dependent surface erosion. While shapes may evolve in a self-similar manner, in neither growth nor erosion can a surface remain invariant. Here we investigate a rare and beautiful geophysical problem that combines both of these processes; the shape evolution of carbonate particles known as ooids. We hypothesize that mineral precipitation, and erosion due to wave-current transport, compete to give rise to novel and invariant geometric forms. We show that a planar (2D) mathematical model built on this premise predicts time-invariant (equilibrium) shapes that result from a balance between precipitation and abrasion. These model results produce nontrivial shapes that are consistent with mature ooids found in nature.