Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T05:29:47.805Z Has data issue: false hasContentIssue false
  • English
  • Français

Symmetry analysis of rotating fluid

Published online by Cambridge University Press:  17 February 2009

K. Fakhar ,
Zu-Chi Chen  and
Xiaoda Ji
K. Fakhar
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China; e-mail: kamranfakhar@yahoo.com.
Zu-Chi Chen
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China; e-mail: kamranfakhar@yahoo.com.
Xiaoda Ji
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China; e-mail: kamranfakhar@yahoo.com.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 1 , July 2005 , pp. 65 - 74
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Bluman, G. W. and Kumei, S., Symmetries and differential equations (Springer, New York, 1989).Google Scholar
[2]Debnath, L., “On unsteady mabnetohydrodynamic boundry layers in a rotating flow”, ZAMM 52 (1972) 623–634.CrossRefGoogle Scholar
[3]Debnath, L., “On Ekman and Hartmann boundry layers in a rotating fluid”, Acta Mech. 18 (1973) 333–340.Google Scholar
[4]Debnath, L., “Resonant oscillations of a porous plate in an electrically conducting rotating viscous fluid”, Phys. Fluids 17 (1974) 1704–1706.CrossRefGoogle Scholar
[5]Debnath, L. and Mukherjee, “Unsteady multiple boundary layers on a porous plate in a rotating system”, Phys. Fluids 16 (1973) 1418–1421.Google Scholar
[6]Fakhar, K., Shagufta, R. and Chen, Z. C., “Lie group analysis of the Navier-Stokes equations in the polar co-ordinates”, IJDEA 7 (2005) 311–323.Google Scholar
[7]Fakhar, K., Shagufta, R. and Chen, Z. C., “Lie group analysis of the axisymmetric flow”, Chaos, Solitons, Fractals 19 (2004) 1261–1267.Google Scholar
[8]Greenspaning, H. P. and Howard, L. N., “On a time dependent motion of a rotating fluid”, J. Fluid. Mech. 17 (1963) 385–396.Google Scholar
[9]Hayat, T., Kara, A. H. and Momoniat, E., “Exact flow of a third-grade fluid on a porous wall”, Int. J. Non-Linear Mech. 38 (2005) 1533–1537.CrossRefGoogle Scholar
[10]Holton, J. R., “The influence of viscous boundry layers on transient motions in a stratified rotating fluid”, Int. J. Atoms. Sci. 22 (1965) 402–412.Google Scholar
[11]Ibragimov, N. H., Elementary Lie group analysis and ordinary differential equations (John Wiley & Sons, New York, 1999).Google Scholar
[12]Momoniat, E., Mason, D. P. and Mahomed, F. M., “Non-linear diffusion of an axisymmetric thin liquid drop: group-invariant solution and conservation law”, Int. J. Non-Linear Mech. 36 (2001) 879–885.Google Scholar
[13]Olver, P. J., Application of Lie Groups to Differential Equations (Springer, Berlin, 1986).Google Scholar
[14]Shercliff, J. A., A Textbook of Magnetohydrodynamics (Pergamon, London, 1965).Google Scholar
[15]Siegmann, W. L., “The spin-down of a rotating stratified fluids”, J. Fluid Mech. 47 (1971) 689–701.CrossRefGoogle Scholar
[16]Walin, G., “Some aspects of a time dependent motion of a stratified rotating fluid”, J. Fluid Mech. 36 (1969) 289–300.Google Scholar
[17]Yürüsory, M., Pakdemirli, M. and Noyan, Ö. F., “Lie group analysis of a creeping flow of a second grade fluid”, Int. J. Non-Linear Mech. 36 (2001) 955–960.CrossRefGoogle Scholar