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Similarity reductions and exact solutions for the two-dimensional incompressible Navier-Stokes equations

Citation

Ludlow, DK and Clarkson, PA and Bassom, AP, Similarity reductions and exact solutions for the two-dimensional incompressible Navier-Stokes equations, Studies in Applied Mathematics, 103, (3) pp. 183-240. ISSN 0022-2526 (1999) [Refereed Article]

Copyright Statement

Copyright 1999 Massachusetts Institute of Technology

DOI: doi:10.1111/1467-9590.00125

Abstract

We study similarity reductions and exact solutions of the (2+1)-dimensional incompressible Navier–Stokes equations using the direct method originally developed by Clarkson and Kruskal [37]. The Navier–Stokes equations are reduced to their conventional stream function form, and it is shown that there exist essentially five reductions into lower-order partial differential equations. Furthermore, we study the possibilities for reducing each of these five forms to ordinary differential equations, some of which can be solved analytically, while others necessitate numerical treatment. In particular we exhibit several new reductions that are not obtained using the classical Lie group method of infinitesimal transformations, and thus we generate new exact solutions of the governing equations. Some of our solutions admit physical interpretations, and many of them contain well-known Navier–Stokes solutions as special examples.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108520
Year Published:1999
Web of Science® Times Cited:31
Deposited By:Mathematics and Physics
Deposited On:2016-04-21
Last Modified:2016-07-08
Downloads:0

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