The theory and application of Navier-Stokeslets (NSlets)

Chadwick, E

Abstract

Consider a closed body moving in an unbounded fluid that decays to rest in the far-field and governed by the
incompressible Navier-Stokes equations. By considering a translating reference frame, this is equivalent to a
uniform flow past the body. A velocity representation is given as an integral distribution of Green’s functions of the
Navier-Stokes equations which we shall call NSlets. The strength of the NSlets is the same as the force distribution
over the body boundary. An expansion for the NSlet is given with the leading-order term being the Oseenlet. To
test the theory, the following three two-dimensional steady flow benchmark applications are considered. First,
consider uniform flow past a circular cylinder for three cases: low Reynolds number; high Reynolds number; and
also intermediate Reynolds numbers at values 26 and 36. These values are chosen because the flow is still steady
and hasn’t yet become unsteady. For low Reynolds number, approximate the NSlet by the leading order Oseenlet
term. For high Reynolds number, approximate the NSlet by the Eulerlet which is the leading order Oseenlet in
the high Reynolds number limit. For the intermediate Reynolds numbers, approximate the NSlet by an Eulerlet
close to its origin, and an Oseenlet further away. Second, consider uniform flow past a slender body with elliptical
cross-section with Reynolds number Re ∼ 10 6 , and approximate the NSlet by the Eulerlet. Finally, consider the Bla-
sius problem of uniform flow past a semi-infinite flat plate and consider the first three terms in the NSlet approximation.

Citation

Chadwick, E. (2019). The theory and application of Navier-Stokeslets (NSlets). Physics of Fluids, 31(10), 107103. https://doi.org/10.1063/1.5119331

• Journal Article Type: Article
• Acceptance Date: Sep 12, 2019
• Online Publication Date: Oct 1, 2019
• Publication Date: Oct 1, 2019
• Deposit Date: Oct 2, 2019
• Publicly Available Date: Oct 2, 2019
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Publisher: AIP Publishing
• Volume: 31
• Issue: 10
• Pages: 107103
• DOI: https://doi.org/10.1063/1.5119331
• Publisher URL: https://doi.org/10.1063/1.5119331
• Related Public URLs: https://aip.scitation.org/journal/phf
• Additional Information: Additional Information : This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Physics of Fluids and may be found at https://doi.org/10.1063/1.5119331.