Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T08:13:41.706Z Has data issue: false hasContentIssue false
  • English
  • Français

Second harmonic resonance in magnetohydrodynamic jet

Published online by Cambridge University Press:  17 February 2009

H. K. Khosla  and
R. K. Chhabra
H. K. Khosla
Affiliation:
Centre for computer Science and Applications, Panjab University, Chandigarh – 160014, India.
R. K. Chhabra
Affiliation:
Dept of Chemical Engineering and Technology, Panjab University, Chandigarh – 160014, India.
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.

Coupled nonlinear partial differential equations, which describe a nonlinear resonant interaction between the fundamental and its first harmonic on a magnetohydro-dynamic jet, are derived by the derivative expansion method. We investigate the spatial behaviour of the amplitude and phases. It is shown that the fluid surface is unstable in the neighbourhood of the first resonant wavenumber. In the steady state, it is observed that the general motion consists of both amplitude and phase modulated waves.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 3 , January 1994 , pp. 323 - 334
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Kakutani, T., Inoue, Y. and Kan, T., “Nonlinear capillary waves on the surface of liquid column”, J. Phys. Soc. Japan 37 (1974) 529–538.CrossRefGoogle Scholar
[2]Lardner, R.W. and Trehan, S.K., “Modulational instability of a magnetohydrodynamic jet”, Astrophys. Space Sci. 96 (1983) 261–281.CrossRefGoogle Scholar
[3]Nayfeh, A.H., “Nonlinear stability of a liquid jet”, Phys. of Fluids 13 (1970) 841–847.CrossRefGoogle Scholar
[4]Nayfeh, A.H. and Hassan, S.D., “The method of multiple scales and nonlinear dispersive waves”, J. Fluid Mech. 48 (1971) 463–475.CrossRefGoogle Scholar
[5]Nayfeh, A.H. and Mook, D., Nonlinear Oscillations (Interscience, 1979).Google Scholar
[6]Rayleigh, Lord, The theory of sound. Volume 2 (Dover Publications, Inc., New York, 1945).Google Scholar
[7]Wang, D.P., “Finite amplitude effect on the stability of a jet of circular cross section”, J. Fluid Mech. 34 (1968) 299–313.CrossRefGoogle Scholar
[8]Yuen, M.C., “Nonlinear capillary instability of a liquid jet” J. Fluid Mech. 33 (1968) 151–163.CrossRefGoogle Scholar