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505_announce - MATH 505 Fall 2007 Mathematical Fluid...

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Unformatted text preview: MATH 505 - Fall 2007 Mathematical Fluid Dynamics Andrew Belmonte † Time: MWF 1:25 - 2:15 PM Location: 322 Sackett Bldg Schedule Number: 869257 This one semester course will provide an introduction to the wide variety of phenomena in fluid dynamics – a subject rich in both mathematical and experimental results and challenges. The course is intended for beginning graduate students in mathematics, physics, engineering, and related fields. After introducing the governing partial differential equations for a flowing continuum (from conservation laws to the stress tensor), we will survey some of the many successes of inviscid fluid dynamics, described by Euler’s equation. We will then introducte the Navier-Stokes equation, and cover some aspects of acoustics and viscous flows. We will also discuss the linear stability of some of the solutions to these equations. Following Prandtl and the development of asymptotic theory, we will discuss boundary layers, and spend some time on turbulence (including Kolmogorov). Our discussion of boundary conditions in thetime on turbulence (including Kolmogorov)....
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