Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Nonlinear electrohydrodynamic instability of a jet

Authors: R. Kant and S. K. Malik
Journal: Quart. Appl. Math. 43 (1986), 407-419
MSC: Primary 76E25; Secondary 76X05
DOI: https://doi.org/10.1090/qam/846153
MathSciNet review: 846153
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Abstract: A weakly nonlinear theory of an electrohydrodynamic jet held together by capillary forces is investigated. The evolution of two-dimensional wave packets on the surface of the jet is shown to be governed by a nonlinear Schrödinger equation. It is found that the wave train of constant amplitude is unstable against modulation. The instability sets in at higher wave numbers as compared to the case of an unelectrified jet.

References [Enhancements On Off] (What's this?)

  • [1] Lord Rayleigh, The theory of sound, Vol. 2, Dover, 1945 MR 0016009
  • [2] J. R. Melcher, Field coupled surface waves, M.I.T. Press, 1963
  • [3] D. H. Michael, Note on the electrostatic instability of a jet, Can. J. Phys. 45, 3179 (1967)
  • [4] M. C. Yuen, Nonlinear capillary instability of a liquid, J. Fluid Mech. 33, 151 (1968)
  • [5] A. H. Nayfeh, Nonlinear stability of a liquid jet, Phys. Fluids 13, 841 (1970)
  • [6] T. Kakutani, Y. Inoue and T. Kan, Nonlinear capillary waves on the surface of liquid column, J. Phy. Soc. Japan 37, 529 (1974)
  • [7] L. Crane, S. Birch and P. D. McCormack, The effect of mechanical vibrations on the break-up of a cylindrical water jet in air, Brit. J. Appl. Phys. 15, 743 (1964)
  • [8] R. J. Donnelly and W. Glaberson, Experiments on the capillary instability of a liquid jet, Proc. Roy. Soc. (London) 290A, 547 (1966)
  • [9] K. C. Chaudhary and T. Maxworthy, The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behaviour before droplet formation, J. Fluid Mech. 96 part 2, 275 (1980)
  • [10] S. K. Malik and M. Singh, Nonlinear break-up of an electrohydrodynamic jet, Quart. Appl. Math. 41, No. 3, 273 (1983) MR 721418
  • [11] J. R. Pierce, An interesting wave amplifier, IRE Transactions on Electron Devices, ED-7, 3 (1960)
  • [12] G. B. Whitman, Linear and nonlinear waves, John Wiley, New York, 1974 MR 0483954
  • [13] V. I. Karpman, Nonlinear waves in dispersive media, Pergamon Press, 1975
  • [14] R. Kant, R. K. Jindia and S. K. Malik, Finite amplitude surface waves in electrohydrodynamics, Quart. Appl. Math. 39, No. 1, 23 (1981)
  • [15] V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Phys., J.E.T.P. 34 (1972) MR 0406174

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DOI: https://doi.org/10.1090/qam/846153
Article copyright: © Copyright 1986 American Mathematical Society

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