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Small disturbances in a conducting fluid in the presence of a current-carrying conductor

Published online by Cambridge University Press:  24 October 2008

A. M. J. Davis
A. M. J. Davis
Affiliation:
St John's College, Cambridge
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Extract

1. Introduction. The problem considered here derives its motivation from a paper by Friedlander (8) on the propagation of small disturbances in a compressible, conducting fluid in the presence of a uniform magnetic field (see also Courant and Hilbert (3), VI, §3a). In this the displacement current and energy dissipation by viscosity, heat conduction and Joule heat are neglected and a system of linear partial differential equations is obtained, which generalizes the equations of motion of the theory of sound. Their solution is in general the superposition of an arbitrary incompressible Alfven wave and a magneto-acoustic disturbance. This latter was considered by constructing a Green's function by means of suitable combinations of plane wave solutions and it was found that there are fast and slow wave fronts diverging from a point disturbance. The latter are conoidal in shape and have a singularity at their vertices which propagate along the field line in either direction from the source.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 2 , April 1964 , pp. 325 - 339
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Bateman, H.Higher transcendental functions. I (McGraw Hill, 1953).Google Scholar
(2)Bazer, J. and Ericson, W.Astr. J. 129 (1959), 758–785.CrossRefGoogle Scholar
(3)Courant, R. and Hilbert, D.Methods of mathematical physics. II (Interscience, 1962).Google Scholar
(4)Cowling, T. G.Magnetohydrodynamics (Interscience, 1957).Google Scholar
(5)Doetsch, G.Guide to the application of Laplace transforms (Van Nostrand, 1961).Google Scholar
(6)Erdélyi, A.Asymptotic expansions (Dover, 1956).Google Scholar
(7)Friedlander, F. G.Comm. Pure Appl. Math.. 7 (1954), 705–732.CrossRefGoogle Scholar
(8)Friedlander, F. G.Proc. Cambridge Philos. Soc.. 55 (1959), 341–367.CrossRefGoogle Scholar
(9)Jeffreys, H.Asymptotic approximations (Cambridge University Press, 1962).Google Scholar
(10)Lamb, H.Hydrodynamics (Cambridge University Press, 6th ed., 1932).Google Scholar
(11)Phillips, E. G.Functions of a complex variable (Oliver and Boyd, 1954).Google Scholar
(12)Rayleigh, LordThe theory of sound. II (Macmillan, 2nd ed. 1896).Google Scholar
(13)Schlesinger, L.Differentialgleichungen Zweite Auflage (Göschen, Leipzig, 1904).Google Scholar