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Fluid Mechanics - A Geometrical Point of View | Oxford Scholarship Online
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Fluid Mechanics: A Geometrical Point of View

S. G. Rajeev

Abstract

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator ... More

Keywords: Euler’s equations, Navier–Stokes equation, shocks, geodesic, curvature, spectral method, Smale’s horse shoe, chaotic advection, renormalization, Feigenbaum–Cvitanovic equation

Bibliographic Information

Print publication date: 2018 Print ISBN-13: 9780198805021
Published to Oxford Scholarship Online: October 2018 DOI:10.1093/oso/9780198805021.001.0001

Authors

Affiliations are at time of print publication.

S. G. Rajeev, author
Professor of Physics and Mathematics, University of Rochester