Skip to main content Accessibility help

The oscillations of a viscous gravitating sphere

  • D. P. McKenzie (a1)


By using a Laplace transformation, a general solution is obtained to the problem of the oscillations and velocity field of a viscous gravitating sphere. Lamb's oscillating solution and Darwin's exponentially decaying solution are derived as asymptotic expressions and their connexion demonstrated. Closed loops of stream lines are a remarkable feature of the flow, and the conditions for their existence are discussed. Asymptotic solutions are also obtained for the oscillations of a Maxwell sphere, and their relation to those of an elastic sphere investigated.



Hide All
(1)Abramowitz, M. and Stegun, I. A.Handbook of mathematical functions (Dover, 1965).
(2)Backus, G.Ann. Phys. 4 (1958), 372447.
(3)Bland, D. R.The theory of linear viscoelasticity (Pergamon, 1960).
(4)Carslaw, H. C. and Jaegar, J. C.Operational methods in applied mathematics (Oxford, 1941).
(5)Darwin, G. H.Philos. Trans. Roy. Soc. London Ser. A 170 (1879), 132.
(6)Gilbert, F.Rev. Geophys. 2 (1964), 123–53.
(7)Lamb, H.Proc. London Math. Soc. 13 (1881), 5166.
(8)Lamb, H.Proc. London Math. Soc. 13 (1882), 189212.
(9)Morse, P. M. and Feshbach, H.Methods of theoretical physics (McGraw-Hill, 1953).
(10)McKenzie, D. P.J. geophys. Res. 71 (1966), 39954010.
(11)Parker, R. L.Proc. Roy. Soc. Ser. A 291 (1966), 6072.
(12)Thomson, W.Philos. Trans. Roy. Soc. London 153 (1863), 583616.

The oscillations of a viscous gravitating sphere

  • D. P. McKenzie (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.