Intervals of electrohydrodynamic Rayleigh-Taylor instability: effect of a normal periodic field

Elshehawey, Elsayed F.

doi:10.1090/qam/1052133

Author: Elsayed F. Elshehawey
Journal: Quart. Appl. Math. 48 (1990), 225-232
MSC: Primary 76E25; Secondary 76W05
DOI: https://doi.org/10.1090/qam/1052133
MathSciNet review: MR1052133
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The intervals of electrohydrodynamic Rayleigh-Taylor instability influenced by a periodic normal field are considered. It is shown that a linear model of the interface is governed by Hill’s differential equation. Characteristic values and intervals of stability are discussed. The special case of Mathieu differential equation type is obtained.

J. R. Melcher, Field Coupled Surface Waves, M.I.T., Cambridge, MA, 1963

J. R. Melcher, Continuum Electromechanics, M.I.T., Cambridge, MA, 1981

H. H. Woodson and J. R. Melcher, Electromechanical Dynamics, part II, John Wiley, New York, 1968

Abou El Magd A. Mohamed and Elsayed F. El Shehawey, Nonlinear electrohydrodynamic Rayleigh-Taylor instability. I. A perpendicular field in the absence of surface charges, J. Fluid Mech. 129 (1983), 473–494. MR 707996, DOI https://doi.org/10.1017/S0022112083000877
Abou El Magd A. Mohamed and Elsayed F. El Shehawey, Nonlinear electrohydrodynamic Rayleigh-Taylor instability. I. A perpendicular field in the absence of surface charges, J. Fluid Mech. 129 (1983), 473–494. MR 707996, DOI https://doi.org/10.1017/S0022112083000877

A. A. Mohamed and E. F. Elshehawey, Nonlinear electrohyrodynamic Rayleigh-Taylor instability. III. Effect of a tangential field, AJSE 9 (4), 345–360 (1984)

Elsayed Elshehawey, Electrohydrodynamic solitons in Kelvin-Helmholtz flow: the case of a normal field in the absence of surface charges, Quart. Appl. Math. 43 (1986), no. 4, 481–499. MR 846159, DOI https://doi.org/10.1090/S0033-569X-1986-0846159-5

E. F. Elshehawey, Y. O. El Dib, and A. A. Mohamed, Electrohydrodynamic stability of a fluid layer. I. Effect of a tangential field, Nuovo Cimento 1 6D, 291–308 (1985)

N. T. El Dabe, E. F. Elshehawey, G. M. Moatimid, and A. A. Mohamed, Electrohydrodynamic stability of two cylindrical interfaces under the influence of a tangential periodic electric field, J. Math. Phys. 26 (8), 2072–2081 (1985)

A. A. Mohamed, E. F. Elshehawey, and Y. O. El Dib, Electrohydrodynamic stability of a fluid layer. II. Effect of a normal electric field, J. Chem. Phys. 85 (1), 445–455 (1986)

A. A. Mohamed, E. F. Elshehawey, and Y. O. El Dib, Electrohydrodynamic stability of a fluid layer. Effect of a tangential periodic field, Nuovo Cimento 1 8D, 177–192, (1986)

U. Zimmerman, Biochim. Biophys. Acta, 694, 227 (1982)

Ali Hasan Nayfeh, Perturbation methods, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. MR 0404788
Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill Book Co., New York, 1978. International Series in Pure and Applied Mathematics. MR 538168
Wilhelm Magnus and Stanley Winkler, Hill’s equation, Dover Publications, Inc., New York, 1979. Corrected reprint of the 1966 edition. MR 559928

E. T. Whittaker and G. N. Watson, Modern Analysis, Cambridge, London-New York, 1927

N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford, at the Clarenden Press, 1947. MR 0021158