Self-similarity of an eroding body

Motivated by the erosion of natural landforms, we study the interaction between an eroding body and surrounding fluid-flow using experiments and simulations. Both reveal the emergence of a unique shape that forms early and then shrinks in a self-similar fashion. Here, I focus on simulations in which erosion rate is dictated by local shear stress. In this high-Reynolds-number context, we determine shear stress by combining an outer, inviscid flow with a boundary layer flow. We discover that a broad range of initial shapes morph into a terminal shape characterized by nearly uniform shear.