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Unformatted text preview: 1 Notes on 1.63 Advanced Environmental Fluid Mechanics Instructor: C. C. Mei, 2001 email@example.com, 1 617 253 2994 September 19, 2002 1-8Rayleigh.tex 1.8 Rayleigh’s Problem - solid wall as a source of vor- ticity Owing to terms representing convective inertia, the Navier-Stokes equations are highly non- linear. Explicit solutions are usually limited to a class of problems where inertia is identically zero. This happens when the f ow is unidirectional and uniform. Flow quantities depend only on a transverse coordinate. We discuss one such example with a view to examining the role of viscosity. Consider a two-dimensional f ow in the upper half plane of ( x, y ) bounded below by a rigid plate coinciding with the x axis. At t = 0 the plate suddenly moves in the tangential direction at constant velocity U . Find the development of the f uid motion in the region y > 0. Because the plate is in F nite in extent, the f ow must be uniform in x , i.e....
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