Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T08:59:06.126Z Has data issue: false hasContentIssue false
  • English
  • Français

The image system of a vortex element in a rigid sphere

Published online by Cambridge University Press:  24 October 2008

M. J. Lighthill
M. J. Lighthill
Affiliation:
The UniversityManchester
Get access Rights & Permissions [Opens in a new window]

Extract

It will be shown that a vortex element has the following image system in a rigid sphere immersed in incompressible fluid:

(i) A transverse vortex element at the inverse point, equal in strength to minus the transverse resultant of the given vortex element, divided by the ratio of its distance from the centre to the radius of the sphere.

(ii) A radial vortex element at the inverse point, equal in strength to plus the radial resultant of the given vortex element, divided by the same ratio.

(iii) A uniform line vortex stretching from the inverse point to the centre of the sphere, equal and opposite in total strength to the radial vortex element at the inverse point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 2 , April 1956 , pp. 317 - 321
Copyright
Copyright © Cambridge Philosophical Society 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Lamb, H.Hydrodynamics, 6th ed. (Cambridge, 1932).Google Scholar
(2)Larmor, J.Quart. J. pure appl. Math. 23 (1889), 94.Google Scholar
(3)Lewis, T. C.Quart. J. pure appl. Math. 16 (1879), 338.Google Scholar
(4)Ludford, G. S. S., Martinek, J. and Yeh, G. C. K.Proc. Camb. phil. Soc. 51 (1955), 389.CrossRefGoogle Scholar
(5)Weiss, P.Proc. Camb. phil. Soc. 40 (1944), 259.CrossRefGoogle Scholar
(6)Young, A. D. and Maas, J. N.Rep. Memor. aero. Res. Comm., Lond., no. 1770 (1936).Google Scholar