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Steady longitudinal motion of an insulating cylinder in a conducting fluid

Published online by Cambridge University Press:  24 October 2008

R. T. Waechter
R. T. Waechter
Affiliation:
School of Physical Sciences, Flinders University, Bedford Park, South Australia
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Abstract

A mathematical analogue between a special class of problems in steady magnetohydrodynamics and appropriate problems in the theory of the scattering of sound pulses is established and exploited. Rigorous asymptotic expansions for large Hartmann number M are obtained for the exact solution of the prototype problem, the circular cylinder. Asymptotic expansions for large M in the case of a cylinder whose cross-section is an arbitrary closed convex curve are obtained as a straightforward application of the theory of geometrical optics and Keller's geometrical theory of diffraction.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 1165 - 1201
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Artmann, K.Z. Physik 127 (1950), 468–494.CrossRefGoogle Scholar
(2)Beckmann, P. and Franz, W.Z. Naturforsch. 12 a (1957), 533–537.CrossRefGoogle Scholar
(3)Braginskii, S. I.Soviet Physics JETP 37 (1960), 1005–1014.Google Scholar
(4)Buchal, R. N. and Keller, J. B.Comm. Pure Appl. Math. 13 (1960), 85–114.CrossRefGoogle Scholar
(5)Childress, S.J. Fluid Mech. 15 (1963), 429–441.CrossRefGoogle Scholar
(6)Eckhaus, W. and de Jager, E. M.Arch. Rational Mech. Anal. 23 (1966), 26–86.CrossRefGoogle Scholar
(7)Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Tables of integral transforms, vol. II (Bateman Manuscript Project, McGraw-Hill, 1954).Google Scholar
(8)Fock, V. A.Electromagnetic diffraction and propagation problems (Pergamon Press, 1965).Google Scholar
(9)Fock, V. A. and Wainstein, L. A.Radiotehn. i Elektron. 8 (1963), 317–341.Google Scholar
(10)Friedlander, F. G.Proc. Cambridge Philos. Soc. 45 (1949), 395–404.CrossRefGoogle Scholar
(11)Friedlander, F. G.Comm. Pure Appl. Math. 7 (1954), 705–732.CrossRefGoogle Scholar
(12)Friedlander, F. G.Sound pulses (Cambridge University Press, 1958).Google Scholar
(13)Greenspan, H. P.J. Fluid Mech. 9 (1960), 454–464.CrossRefGoogle Scholar
(14)Grimshaw, R.Comm. Pure Appl. Math. 19 (1966), 167–198.CrossRefGoogle Scholar
(15)Grinberg, G. A.J. Appl. Math. Mech. 25 (1961), 1536–1550.CrossRefGoogle Scholar
(16)Grinberg, G. A.J. Appl. Math. Mech. 26 (1962), 106–117.CrossRefGoogle Scholar
(17)Hadamard, J.Lectures on Cauchy's problem (Yale University Press, 1923).Google Scholar
(18)Hasimoto, H.J. Fluid Mech. 8 (1960), 61–81.CrossRefGoogle Scholar
(19)Jones, S. D.Proc. Roy. Soc. Ser. A 239 (1957), 338–348.Google Scholar
(20)Keller, J. B.Proc. Symp. Appl. Math. vol. VIII (ed. Graves, L. M., New York, 1958).Google Scholar
(21)Levy, B. and Keller, J. B.Comm. Pure Appl. Math. 12 (1959), 159–209.CrossRefGoogle Scholar
(22)Lewis, R. M.Proceedings of Symposium in Quasi-optics, pp. 71–103 (Polytechnic Press. Brooklyn, 1964).Google Scholar
(23)Mie, G.Ann. Physik 25 (1908), 377.CrossRefGoogle Scholar
(24)Miller, J. C. P.The Airy integral (Brit. Ass. Math. Tables Committee, 1946.)Google Scholar
(25)Nussenzveig, H. M.Ann. Physics 34 (1965), 23–95.CrossRefGoogle Scholar
(26)Olver, F. W. J.Philos. Trans. Roy. Soc. London, Ser. A 247 (1954), 328–368.Google Scholar
(27)Papadopoulos, V. M.Div. Eng. Brown Univ., Sc. Rep. 1391/10, 1958.Google Scholar
(28)Rubinow, S. I. and Keller, J. B.J. Appl. Phys. 32 (1961), 814–820.CrossRefGoogle Scholar
(29)Shercliff, J. A.Proc. Cambridge Philos. Soc. 49 (1953), 136–144.CrossRefGoogle Scholar
(30)Shercliff, J. A.J. Fluid Mech. 13 (1962), 513–518.CrossRefGoogle Scholar
(31)Todd, L.J. Fluid Mech. 28 (1967), 371–384.CrossRefGoogle Scholar
(32)Ursell, F.Proc. Cambridge Philos. Soc. 53 (1957), 115–133.CrossRefGoogle Scholar
(33)Van de Hulst, H. C.Physica 15 (1949), 740–746.CrossRefGoogle Scholar
(34)Waechter, R. T. Ph.D. Dissertation, Cambridge, 1966.Google Scholar
(35)Zauderer, E.J. Math. Mech. 13 (1964), 171–186.Google Scholar