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On the equations of Vortex motion, with special reference to the use of polar co-ordinates

Published online by Cambridge University Press:  20 January 2009

C. Chree
C. Chree
Affiliation:
King' College, Cambridge.
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In several previous communications to the Society, I have considered the equations of vortex motion in two dimensions in a compressible fluid. In the present communication I propose to consider certain forms of the hydro-dynamical equations of a more general kind. In certain cases the fluid will be supposed to be rotating, prior to the introduction of the vortex motion, with uniform angular velocity about a fixed axis.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 8 , February 1889 , pp. 43 - 64
Copyright
Copyright © Edinburgh Mathematical Society 1889

References

* Proceedings, vol. V., p. 52;Google Scholar vol. VI., p. 59; vol. VII., p. 29.

† Proceedings, vol. VII., p. 29.Google Scholar

* See Proceedings, vol. VII., p. 32.Google Scholar

† Lamb's Motion of Fluids, Note D.

* Vol. II., Art. 470.

† Vol. III., p. 109.

* Proceedings, Vol. III., p. 113.Google Scholar Cf. Basset's, Treatise on Hydrodynamics, Vol. I., Art. 18.Google Scholar

* Treatise on the Motion of Fluids, Art. 129.

* Cf. Basset's Art. 95.

† Second Edition. In the first edition change µ into 1/µ in these equations and in Art. 617.

* Quarterly Journal, Vol. xvi., p. 338,Google Scholar or Basset's, Art. 311, Vol.ii.Google Scholar

† Phil. Trans. 1880, Part ii., p, 455,Google Scholar or Basset's, Art. 52, Vol. i.Google Scholar

* Proceedings, Vol. vi., p. 65.Google Scholar