# Applied/ACMS/absF17

# ACMS Abstracts: Fall 2017

### Jinzi Mac Huang (Courant)

*Non-hydrostatic extension of classical shallow-water models*

In geology, dissolution in fluids leads to natural pattern formations. For example the Karst topography occurs when water dissolves limestone, and travertine terraces form as a balance of dissolution and precipitation. In this talk, we consider the shape dynamics of a soluble object immersed in water, with either external flow imposed or convective flow under gravity. We find that different flow configurations lead to different shape dynamics, for example a terminal self-similar shape emerges from dissolving in external flow, while fine scale patterns form when no external flow is imposed. We also find that under gravity, a dissolving body with initially smooth surface evolves into an increasingly sharp needle shape. A mathematical model predicts that a geometric shock forms at the tip of dissolved body, with the tip curvature becoming infinite in finite time.