Guillaume van Baalen 2002 Nonlinearity 15 315 doi:10.1088/0951-7715/15/2/306
Guillaume van Baalen
Show affiliationsRecommended by W J Zakrzewski
We consider stationary solutions of the incompressible Navier-Stokes equations for exterior domains in two dimensions with a non-zero asymptotic flow u∞ at infinity. Under the restriction that the obstacle (the complement of the exterior domain) is symmetric around an axis parallel to u∞, we prove that asymptotically in the down-stream direction, the leading-order deviation from the constant flow approaches a universal shape which depends only on one parameter, namely the net force exerted by the fluid on the obstacle in the direction of u∞. To get this result, we show that the (elliptic) Navier-Stokes equations can be interpreted as a dynamical system, the down-stream direction playing the role of time, which shares some aspects with a parabolic partial differential equation.
47.10.ad Navier-Stokes equations
76D05 Navier-Stokes equations (See also 35Q30)
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
Issue 2 (March 2002)
Received 27 February 2001, in final form 11 December 2001
Published 11 February 2002
Guillaume van Baalen 2002 Nonlinearity 15 315
Dénes Molnár 2005 J. Phys. G: Nucl. Part. Phys. 31 S421
A Burdakin et al 2008 Metrologia 45 75
Katsuhiro Yokota et al 2004 J. Phys. D: Appl. Phys. 37 1095
H Baumann et al 2009 Metrologia 46 178
Erich Gaertig and Kostas D Kokkotas 2009 J. Phys.: Conf. Ser. 189 012016
2005 J. Radiol. Prot. 25 101
Habib Ammari et al 2005 J. Phys.: Conf. Ser. 12 13
P E de Brito and H N Nazareno 2007 Eur. J. Phys. 28 9
S R Gocić et al 2009 J. Phys. D: Appl. Phys. 42 212001