Solitary waves on a conducting fluid layer. (English) Zbl 0654.76105
The effect of an electric field on the long wave motion of the surface of a conducting fluid layer is considered. A Korteweg-de Vries-type equation with coefficients depending on the applied field is derived. The speed of the solitary wave on the fluid layer is seen to be reduced by the electric field. It is found that there are two critical values of the applied voltage that lead to (i) breaking up of the solitary waves and (ii) bifurcation of solutions of the governing equations. For a given value of the imposed potential, solitary waves of elevation and depression are possible depending on the value of surface tension.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76B25 | Solitary waves for incompressible inviscid fluids |
| 35Q30 | Navier-Stokes equations |
References:
| [1] | Lord Rayleigh,The Theory of Sound(Macmillan, New York, 1894). · JFM 25.1604.01 |
| [2] | Michael, Q. Appl. Math. 35 pp 345– (1977) |
| [3] | Sivamoggi, Q. Appl. Math. 37 pp 424– (1979) |
| [4] | Kant, Q. Appl. Math. 38 pp 23– (1981) |
| [5] | Hunter, J. Fluid Mech. 134 pp 205– (1983) |
| [6] | Aoyama, J. Phys. Soc. Jpn. 42 pp 313– (1977) |
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