A radiation-conditioned Gaussian induced MGD conefield
Author:
Lim Chee-seng
Journal:
Quart. Appl. Math. 35 (1977), 321-335
DOI:
https://doi.org/10.1090/qam/99644
MathSciNet review:
QAM99644
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Abstract: Explicit radiation-conditioned solutions are derived for magnetically-aligned MGD flow past a Gaussian source. If the latter’s principal dimension is small, then corresponding to a supersonic-superAlfvénic (or restricted subsonic-subAlfvénic) flow, a strong perturbation field is encountered downstream from a downstream (or upstream from an upstream) tangent cone to the “fast” sheet (or one of the two “slow” cusped sheets) of the Friedrichs wavefront, while a weak estimable field appears upstream (or downstream) from this cone. The strong field is represented by an expansion with accessible asymptotic development. For a finite principal source dimension, other asymptotic modes can be extracted from a separate uniformly valid formulation. In particular, the asymptotic behavior near the dividing tangent cone is nonsingular and suggests the possible existence there of a conical sheath within which the field is probably most concentrated, and across which its transition from strong to weak occurs gradually.
- Chee Seng Lim, A two-dimensional field induced by travelling sources, Quart. J. Mech. Appl. Math. 26 (1973), 371–395. MR 337128, DOI https://doi.org/10.1093/qjmam/26.3.371
- Chee Seng Lim, Axial radiation reception, Proc. Cambridge Philos. Soc. 74 (1973), 369–395. MR 325019, DOI https://doi.org/10.1017/s0305004100048143
- G. D. Crapper, A three-dimensional solution for waves in the lee of mountains, J. Fluid Mech. 6 (1959), 51–76. MR 108367, DOI https://doi.org/10.1017/S0022112059000490
- G. D. Crapper, Steady magnetogasdynamic flow past a source, J. Inst. Math. Appl. 1 (1965), 241–257. MR 191250
E. Cumberbatch, J. Aerospace Sci. 29, 1476 (1962)
- Horace Lamb, Hydrodynamics, 6th ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1993. With a foreword by R. A. Caflisch [Russel E. Caflisch]. MR 1317348
- M. J. Lighthill, Studies on magneto-hydrodynamic waves and other anisotropic wave motions, Philos. Trans. Roy. Soc. London Ser. A 252 (1960), 397–430. MR 148337, DOI https://doi.org/10.1098/rsta.1960.0010
- M. J. Lighthill, Group velocity, J. Inst. Math. Appl. 1 (1965), 1–28. MR 184458
M. J. Lighthill, J. Fluid Mech. 27, 725 (1967)
W. R. Sears and E. L. Resler, Advances in Applied Mechanics 8, Academic Press, New York, 1964
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
L. Chee-Seng, Q.J. Mech. Appl. Math. 26, 371 (1973)
L. Chee-Seng, Proc. Camb. Phil. Soc. 74, 369 (1973)
G. D. Crapper, J. Fluid Mech. 6, 51 (1959)
G. D. Crapper, J. Inst. Math. Applies. 1, 241 (1965)
E. Cumberbatch, J. Aerospace Sci. 29, 1476 (1962)
H. Lamb, Hydrodynamics, 6th ed., Cambridge University Press, 1932
M. J. Lighthill, Phil. Trans. Roy. Soc. London A252, 397 (1960)
M. J. Lighthill, J. Inst. Math. Applies. 1, 1 (1965)
M. J. Lighthill, J. Fluid Mech. 27, 725 (1967)
W. R. Sears and E. L. Resler, Advances in Applied Mechanics 8, Academic Press, New York, 1964
G. N. Watson, Theory of Bessel functions, 2nd ed. Cambridge University Press, 1944 (reissued in paperback, 1966)
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Article copyright:
© Copyright 1977
American Mathematical Society
