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On the existence of an exact solution of the Navier-Stokes equation pertaining to certain vortex motion

Published online by Cambridge University Press:  09 April 2009

K. Kuen Tam
K. Kuen Tam
Affiliation:
Department of Mathematics, McGill UniversityMontreal, Quebec
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In 1942, Burgers [1] observed that in cylindrical polar coordinates, the steady Navier-Stokes equation governing viscous incompressible fluid motion can be reduced to a set of ordinary differential equations if the velocity components vr, vo and vz are assumed to have a special form.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 4 , June 1972 , pp. 456 - 460
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Burgers, J. M., ‘Application of a model system to illustrate some points of the statistical theory of free turbulence’, Proc. Acad. Sci. Amsterdam 43 (1940), 2–12.Google Scholar
[2]Donaldson, C. Du P. and Sullivan, R. D., ‘Behaviour of solutions of the Navier-Stokes equations for a complete class of three-dimensional viscous vortices’, Proc. Heat Transfer and Fluid Mech. (1960), 16–30.Google Scholar
[3]Ho, D. and Wilson, H. K., ‘On the existence of a similarity solution for a compressible boundary layer’. Arch. Rational Mech. Anal. 27 (1967), 165–174.Google Scholar
[4]McLeod, J. B. and Serrin, J., ‘The existence of similar solutions for some laminar boundary layer problem’. Arch. Rational Mech. Anal. 31 (1968), 288–303.CrossRefGoogle Scholar