Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Effects of gravitational or electromagnetic fields on fluid motion.


Author: Chia-Shun Yih
Journal: Quart. Appl. Math. 16 (1959), 409-415
MSC: Primary 76.00
DOI: https://doi.org/10.1090/qam/103027
MathSciNet review: 103027
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Abstract: It is shown in this paper that the effect of gravity on a stratified fluid is to inhibit steady motion in the direction of gravity; that, for small values of the magnetic viscosity, the effect of a main magnetic field is to make steady weak motions of a fluid independent of the distance along the lines of force; and that, again for small values of the magnetic viscosity, the effect of a uniform electric field is to make steady weak motions of a fluid rotationally symmetric with respect to an axis in the direction of the field. These results, together with a similar one of Proudman (1916) [1] for a fluid with general rotation, enable one to state that the effects of rotation, gravity, and electromagnetic fields (for small magnetic viscosity) are to endow the fluid with a certain anisotropic rigidity by ``stiffening'' it along the vorticity lines, the isopycnic surfaces or lines, or the lines of force, as the case may be. In the case of a weak steady motion or relative motion, this ``stiffening'' has the effect of reducing the a priori number of physical or at least mathematical dimensions of the motion by one.


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

  • [1] J. Proudman, On the motion of solids in a liquid possessing vorticity, Proc. Roy. Soc. A92, 408-24 (1916)
  • [2] Sir Geoffrey Taylor, Experiments on the motion of solid bodies in rotating fluids, Proc. Roy. Soc. A104, 213-18 (1923)
  • [3] R. R. Long, Steady motion around a symmetrical obstacle moving along the axis of a rotating fluid, J. Met. 10, 197-203 (1953)
  • [4] G. W. Morgan, A study of motions in a rotating liquid, Proc. Roy. Soc. London. Ser. A. 206 (1951), 108–130. MR 0042239, https://doi.org/10.1098/rspa.1951.0059
  • [5] Paul Gariél, Recherches experimentales sur l'écoulement de couches superposées de fluides de densités differentes, La Houille Blanche, No. 1, 56-64 (1949)
  • [6] T. G. Cowling, Magnetohydrodynamics, Interscience Tracts on Physics and Astronomy, No. 4, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1957. MR 0098556

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DOI: https://doi.org/10.1090/qam/103027
Article copyright: © Copyright 1959 American Mathematical Society


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