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Self-similar evolution of a body eroding in a fluid flow
6. S. Wang, “Coastal hoodoos,” Encyclopedia of Coastal Science (Springer, Netherlands, 2005), pp. 260–262.
8. H. C. Groen, F. J. Gijsen, A. van der Lugt, M. S. Ferguson, T. S. Hatsukami, A. F. van der Steen, C. Yuan, and J. J. Wentzel, “Plaque rupture in the carotid artery is localized at the high shear stress region: A case report,” Stroke 38, 2379–2381 (2007).
10. G. Nanz and L. E. Camilletti, “Modeling of chemical-mechanical polishing: A review,” IEEE Trans. Semiconduct. Manuf. 8, 382–389 (1995).
11. S. Gupta, The Classical Stefan Problem: Basic Concepts, Modelling and Analysis (Elsevier, Amsterdam, 2003).
12. L. Ristroph, M. Moore, S. Childress, M. Shelley, and J. Zhang, “Sculpting of an erodible body by flowing water,” Proc. Natl. Acad. Sci. U.S.A. 109, 19606–19609 (2012).
13. H. Helmholtz, “Über diskontinuierliche Flüssigkeitsbewegungen” Philos. Mag. 36, 337–346 (1868).
17. H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1960).
18. C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics (Oxford University Press, New York, 1997).
19. V. V. Sychëv, A. I. Ruban, V. V. Sychev, and G. L. Korolev, Asymptotic Theory of Separated Flows (Cambridge University Press, Cambridge, 1998).
21. S. Alben, M. Shelley, and J. Zhang, “How flexibility induces streamlining in a two-dimensional flow,” Phys. Fluids 16, 1694–1713 (2004).
25. M. Brillouin, “Les surfaces de glissement d'Helmholtz et la résistance des fluides,” Ann. Chim. Phys. 23, 145–230 (1911).
26. H. Villat, “Sur la validité des solutions de certains problèmes d'hydrodynamique,” J. Math. Pures Appl. 10, 231–290 (1914).
30. J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (Cambridge University Press, Cambridge, 1999), Vol. 3.
32.Here we normalize time by , where cm/hr for the experiments, as opposed to normalizing by tf. The quantity t* estimates the vanishing time in the case of no erosion on the backside of the body, allowing a more faithful comparison between the experimental and simulated front evolution.
36. W. P. Graebel, Engineering Fluid Mechanics (Taylor and Francis, New York, 2001).
38. A. Fowler, “Dunes and drumlins,” Geomorphological Fluid Mechanics (Springer, Berlin, 2001), pp. 430–454.
43. J. T. Hack, “Dynamic equilibrium and landscape evolution,” Theories of Landform Development (State University of New York, 1975), pp. 87–102.
45. D. Burbank, A. Blythe, J. Putkonen, B. Pratt-Sitaula, E. Gabet, M. Oskin, A. Barros, and T. Ojha, “Decoupling of erosion and precipitation in the Himalayas,” Nature (London) 426, 652–655 (2003).
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Erosion of solid material by flowing fluids plays an important role in shaping landforms, and in this natural context is often dictated by processes of high complexity. Here, we examine the coupled evolution of solid shape and fluid flow within the idealized setting of a cylindrical body held against a fast, unidirectional flow, and eroding under the action of fluid shear stress. Experiments and simulations both show self-similar evolution of the body, with an emerging quasi-triangular geometry that is an attractor of the shape dynamics. Our fluid erosion model, based on Prandtl boundary layer theory, yields a scaling law that accurately predicts the body's vanishing rate. Further, a class of exact solutions provides a partial prediction for the body's terminal form as one with a leading surface of uniform shear stress. Our simulations show this predicted geometry to emerge robustly from a range of different initial conditions, and allow us to explore its local stability. The sharp, faceted features of the terminal geometry defy the intuition of erosion as a globally smoothing process.
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