Conically similar viscous flows. Part 2. One-parameter swirl-free flows

Paull R. and Pillow A.F. (1985) Conically similar viscous flows. Part 2. One-parameter swirl-free flows. Journal of Fluid Mechanics, 155 343-358. doi:10.1017/S0022112085001847

Author Paull R.
Pillow A.F.
Title Conically similar viscous flows. Part 2. One-parameter swirl-free flows
Journal name Journal of Fluid Mechanics   Check publisher's open access policy
ISSN 1469-7645
Publication date 1985-01-01
Sub-type Article (original research)
DOI 10.1017/S0022112085001847
Volume 155
Start page 343
End page 358
Total pages 16
Subject 2210 Mechanical Engineering
2211 Mechanics of Materials
3104 Condensed Matter Physics
2206 Computational Mechanics
3100 Physics and Astronomy
Abstract It was shown in Part 1 of this series that in swirl-free flow there are three different types of axial causes of steady conically similar viscous flow. The three corresponding swirl-free one-parameter families of exact solutions to the Navier-Stokes equations are presented and analysed here in terms of the basic conservation principles for volume and ring circulation. The simplest is the irrotational flow generated by a uniform distribution of volume sources along a half-axis. A second, independent, one-parameter family of solutions is provided by Landau's (1943) solution, where the second moment of ring circulation about the axis is produced at the origin at a finite constant rate. Fresh insight into the nature of this flow is gained by separating and comparing the roles of the diffusion and convection terms in the flux vector for ring circulation. A similar analysis is applied to the remaining independent one-parameter family caused by an antisymmetric (about the origin) conically similar axial distribution of the singularity in Landau's solution. This simple new family of exact solutions is characterized by opposed jets neighbouring the axis of symmetry. When the axial jets are directed inwards, they always erupt into an emergent axisymmetric jet normal to the axis of symmetry. Solutions fail to exist, however, for sufficiently strong axial jets directed outwards.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
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Citation counts: Scopus Citation Count Cited 8 times in Scopus Article | Citations
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Created: Sat, 09 Jul 2016, 17:04:54 EST by System User