Sculpting of an erodible body by flowing water

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.

流动的流体的侵蚀在地球上雕刻出引人注目的地貌，也为其他星球过去和现在的环境提供了重要线索。在这些过程中，固体边界既影响周围的流体，又被周围的流体所塑造，但这种相互作用所导致的形态的形成还没有被很好地理解。我们研究了由黏土制成并沉浸在快速单向水流中的可侵蚀物体在形状和水流方面的共同演化。尽管侵蚀通常被视为一种平滑过程，但我们发现，随着固体缩小，侵蚀会塑造出尖锐的和角状的特征并持续存在。我们利用流动可视化和一个流体力学模型来解释这些观察结果，在该模型中，表面剪切应力决定了物质去除的速率。实验和模拟表明，这种相互作用最终导致边界以自相似的方式后退，并形成一个独特的前表面，其特征是几乎均匀的剪切应力。这种应力趋于一致的趋势为理解更复杂的几何形状和流动（比如自然界中存在的那些）中的侵蚀提供了一个原理。