Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF Free Access

Abstract | References | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] L. Chee-Seng, Q.J. Mech. Appl. Math. 26, 371 (1973) MR 0337128
  • [2] L. Chee-Seng, Proc. Camb. Phil. Soc. 74, 369 (1973) MR 0325019
  • [3] G. D. Crapper, J. Fluid Mech. 6, 51 (1959) MR 0108367
  • [4] G. D. Crapper, J. Inst. Math. Applies. 1, 241 (1965) MR 0191250
  • [5] E. Cumberbatch, J. Aerospace Sci. 29, 1476 (1962)
  • [6] H. Lamb, Hydrodynamics, 6th ed., Cambridge University Press, 1932 MR 1317348
  • [7] M. J. Lighthill, Phil. Trans. Roy. Soc. London A252, 397 (1960) MR 0148337
  • [8] M. J. Lighthill, J. Inst. Math. Applies. 1, 1 (1965) MR 0184458
  • [9] M. J. Lighthill, J. Fluid Mech. 27, 725 (1967)
  • [10] W. R. Sears and E. L. Resler, Advances in Applied Mechanics 8, Academic Press, New York, 1964
  • [11] G. N. Watson, Theory of Bessel functions, 2nd ed. Cambridge University Press, 1944 (reissued in paperback, 1966) MR 0010746

Additional Information

DOI: https://doi.org/10.1090/qam/99644
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society