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Simple Viscous Flows: from Boundary Layers to the Renormalization Group

Authors
  • Veysey, John
  • Goldenfeld, Nigel
Type
Preprint
Publication Date
Jan 22, 2007
Submission Date
Sep 15, 2006
Identifiers
DOI: 10.1103/RevModPhys.79.883
Source
arXiv
License
Unknown
External links

Abstract

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics.

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