Applied Mathematics Laboratory, Courant Institute, New York University, New York, NY 10012, USA.
Proc Natl Acad Sci U S A. 2012 Nov 27;109(48):19606-9. doi: 10.1073/pnas.1212286109. Epub 2012 Nov 12.
Erosion by flowing fluids carves striking landforms on Earth and also provides important clues to the past and present environments of other worlds. In these processes, solid boundaries both influence and are shaped by the surrounding fluid, but the emergence of morphology as a result of this interaction is not well understood. We study the coevolution of shape and flow in the context of erodible bodies molded from clay and immersed in a fast, unidirectional water flow. Although commonly viewed as a smoothing process, we find that erosion sculpts pointed and cornerlike features that persist as the solid shrinks. We explain these observations using flow visualization and a fluid mechanical model in which the surface shear stress dictates the rate of material removal. Experiments and simulations show that this interaction ultimately leads to self-similarly receding boundaries and a unique front surface characterized by nearly uniform shear stress. This tendency toward conformity of stress offers a principle for understanding erosion in more complex geometries and flows, such as those present in nature.
流动的流体侵蚀会在地球上形成引人注目的地貌，也为其他行星过去和现在的环境提供了重要线索。在这些过程中，固体边界不仅会影响周围的流体，还会被其塑造，但这种相互作用导致的形态的出现还没有得到很好的理解。我们研究了在快速单向水流中浸泡的由粘土制成的可变形体的形状和流动的协同演变。尽管通常被视为平滑过程，但我们发现侵蚀会塑造出尖锐和棱角分明的特征，这些特征在固体收缩时仍然存在。我们使用流动可视化和一个流体力学模型来解释这些观察结果，其中表面剪切应力决定了材料去除的速度。实验和模拟表明，这种相互作用最终导致自相似的后退边界和具有几乎均匀剪切应力的独特前表面。这种对应力一致性的趋势为理解更复杂的几何形状和流动中的侵蚀提供了一个原则，例如自然界中存在的侵蚀。
