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Exploration of Fluid Meandering by Statistical Simulation

Fluid meanders, such as river meandering, fluid intrusions, and microscopic flows over a surface, are difficult to model from classical dynamics. Another approach is to select trajectories from a randomly generated sample. This Demonstration generates individual trajectories with a few controls. The simulated process is a fluid bead sliding down a surface dominated by friction. There are occasional lateral displacements from a choice of distributions. For some choices of parameters, the courses, outlined by the extremes of the trajectory, look very much like meanders.

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"Up a Lazy River" is the American Scientist article that got me thinking about the problem. Albert Einstein wrote on this topic; see "The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer’s Law". There is a mathematical model in "River Meandering and a Mathematical Model of this Phenomenon".
References:
B. Hayes, "Up a Lazy River," American Scientist, 94(6), 2006 pp. 490–494.
A. Einstein, "The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer’s Law," Die Naturwissenschaften, 14, 1926.
N. Movshovitz-Hadar and A. Shmukler, "River Meandering and a Mathematical Model of This Phenomenon," PhysicaPlus, No. 7, 2006.
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