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Fluid DynamicsPart 1: Classical Fluid Dynamics$
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Anatoly I. Ruban and Jitesh S. B. Gajjar

Print publication date: 2014

Print ISBN-13: 9780199681730

Published to Oxford Scholarship Online: August 2014

DOI: 10.1093/acprof:oso/9780199681730.001.0001

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Solutions of the Navier–Stokes Equations

Solutions of the Navier–Stokes Equations

(p.95) 2 Solutions of the Navier–Stokes Equations
Fluid Dynamics

Anatoly I. Ruban

Jitesh S. B. Gajjar

Oxford University Press

This chapter describes solutions of the Navier–Stokes equations, starting with simple physical situations where these equations allow exact solutions, i.e. solutions in analytic form. These include Couette flow between two parallel plates, Hagen–Poiseuille flow through a pipe, flow above an impulsively started plate (where the notion of a self-similar solution and the Stokes layer are introduced), dissipation of the potential vortex caused by fluid viscosity, and Kármán flow above an infinite rotating disk. Some numerical solutions of the Navier–Stokes equations are then presented to illustrate various important properties of viscous flows. Flow past a circular cylinder is examined, and it is shown what happens to the separation eddy region behind the cylinder as the Reynolds number increases. The behaviour of flow in a cavity is also discussed, and it is demonstrated how recirculating eddies can multiply as the fluid viscosity decreases.

Keywords:   exact solutions, Couette flow, Hagen–Poiseuille flow, Kármán flow, Stokes layer, dissipation of potential vortex

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