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

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

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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.

**[1]**J. R. Melcher,*Field Coupled Surface Waves*, M.I.T., Cambridge, MA, 1963**[2]**J. R. Melcher,*Continuum Electromechanics*, M.I.T., Cambridge, MA, 1981**[3]**H. H. Woodson and J. R. Melcher,*Electromechanical Dynamics*, part II, John Wiley, New York, 1968**[4]**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**, https://doi.org/10.1017/S0022112083000877**[5]**Abou El Magd A. Mohamed and Elsayed F. El Shehawey,*Nonlinear electrohydrodynamic Rayleigh-Taylor instability. II. A perpendicular field producing surface charge*, Phys. Fluids**26**(1983), no. 7, 1724–1730. MR**710076**, https://doi.org/10.1063/1.864371**[6]**A. A. Mohamed and E. F. Elshehawey,*Nonlinear electrohyrodynamic Rayleigh-Taylor instability*. III.*Effect of a tangential field*, AJSE**9**(4), 345-360 (1984)**[7]**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**, https://doi.org/10.1090/S0033-569X-1986-0846159-5**[8]**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)**[9]**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)**[10]**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)**[11]**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)**[12]**U. Zimmerman, Biochim. Biophys. Acta, 694, 227 (1982)**[13]**Ali Hasan Nayfeh,*Perturbation methods*, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. MR**0404788****[14]**Philip M. Morse and Herman Feshbach,*Methods of theoretical physics. 2 volumes*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR**0059774****[15]**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****[16]**Wilhelm Magnus and Stanley Winkler,*Hill’s equation*, Dover Publications, Inc., New York, 1979. Corrected reprint of the 1966 edition. MR**559928****[17]**E. T. Whittaker and G. N. Watson,*Modern Analysis*, Cambridge, London-New York, 1927**[18]**N. W. McLachlan,*Theory and Application of Mathieu Functions*, Oxford, at the Clarenden Press, 1947. MR**0021158**

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DOI:
https://doi.org/10.1090/qam/1052133

Article copyright:
© Copyright 1990
American Mathematical Society