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The flow created by a sphere moving along the axis of a rotating, slightly-viscous fluid

Published online by Cambridge University Press:  29 March 2006

T. Maxworthy
T. Maxworthy
Affiliation:
Geophysical Fluid Dynamics Laboratory, University of Southern California, Los Angeles
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Abstract

The title flow has been studied by measuring the drag force on, and by observing the flow field around, a sphere rising through a large, rotating tank of water. Long, almost stagnant, regions are formed up- and downstream within the shadow of the sphere and are surrounded by a thin annular region within which the velocity is larger than the mean velocity of the approach flow. Several regions are found within which vortex-jump phenomena occur and it is concluded that such features exert a controlling influence over the dynamics of the observed flow field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 40 , Issue 3 , 18 February 1970 , pp. 453 - 479
Copyright
© 1970 Cambridge University Press

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References

Benjamin, T. B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14, 593.Google Scholar
Benjamin, T. B. 1967 Some developments in the theory of vortex breakdown. J. Fluid Mech. 28, 65.Google Scholar
Bossel, H. H. K. 1967 Inviscid and viscous models of the vortex breakdown phenomenon. Report no. AS-67-A, College of Engineering, University of California, Berkeley.
Bretherton, F. P. 1967 The time dependent motion due to a cylinder moving in an unbounded rotating or stratified fluid. J. Fluid Mech. 28, 545.Google Scholar
Childress, W. S. 1962 Rotating, viscous flow past an axially symmetric solid. Jet Prop. Lab. Space Prog. Sum. no. 37–18, IV, 46–48.Google Scholar
Childress, W. S. 1964 The slow motion of a sphere in a rotating, viscous fluid. J. Fluid Meck. 20, 305Google Scholar
Gracb, S. F. 1926 On the motion of a sphere in a rotating liquid. Proc. Roy. Soc. Lond. A 113, 46.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Janowitz, G. S. 1968 On wakes in stratified fluids. J. Fluid Mech. 33. 417.Google Scholar
Küchemann, D. 1965 Report on the I.U.T.A.M. symposium on concentrated vortex motions in fluids. J. Fluid Mech. 21, 1.Google Scholar
Long, R. R. 1953 Steady motion around a symmetrical obstacle moving along the axis of a rotating fluid. J. Met. 10, 197.Google Scholar
Martin, S. & Long, R. R. 1968 The slow motion of a flat plate in a viscous, stratified fluid. J. Fluid Mech. 31, 669.Google Scholar
Maxworthy, T. 1965 An experimental determination of the slow motion of a sphere in a rotating, viscous fluid. J. Fluid Mech. 23. 373.Google Scholar
Maxworthy, T. 1967 The flow creating a concentration of vorticity over a stationary plate. Jet Prop. Lab. Space Prog. Sum. no. 37–44, IV, 243–249.Google Scholar
Maxworthy, T. 1968a Experimental studies in magneto-fluid dynamics: pressure distribution measurements around a sphere. J. Fluid Mech. 31, 801.Google Scholar
Maxworthy, T. 1968b The observed motion of a sphere through a short, rotating cylinder of fluid. J. Fluid Mech. 31, 643.Google Scholar
Miles, J. W. 1968a Lee waves in a stratified flow. Part I. Thin barrier. J. Fluid. Mech. 32, 549.Google Scholar
Miles, J. W. 1968b Lee waves in a stratified flow. Part II. Semi-circular obstacle. J. Fluid Mech. 33, 803.Google Scholar
Miles, J. W. 1969a The lee-wave régime for a slender body in a rotating fluid. J. Fluid Mech. 36, 265.Google Scholar
Miles, J. W. 1969b Axisymmetric flow of a rotating, viscous liquid over a given stream surface. J. Fluid Mech. (To be published.)Google Scholar
Moore, D. W. & Saffman, P. G. 1968 The rise of a body through a rotating fluid in a container of finite length. J. Fluid Mech. 31, 635.Google Scholar
Moore, D. W. & Saffman, P. G. 1969 The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body. Trans. Roy. Soc. Lond. A 264, 597.Google Scholar
Morrison, J. W. & Morgan, G. W. 1956 The slow motion of a disk along the axis of viscous, rotating liquid. Report 56207/8, Div. of Appl. Math. Brown University.
Pao, H. H. 1968 Laminar flow of a stably stratified fluid past a flat plate. J. Fluid Mech. 34, 795.Google Scholar
Proudman, J. 1916 On the motion of solids in a liquid possessing vorticity. Proc. Roy. Soc. Lond. A 92, 408.Google Scholar
Rott, N. & Lewellen, W. S. 1966 Boundary layers in rotating flows. In Progress in Aeronautical Sciences, vol. 7. Oxford: Pergamon.
Schraub, F. A., Kline, S. J., Henry, H., Runstadler, P. W. & Pittell, A. 1965 Trans A.S.M.E. Ser. D, 87, 429.
Squire, H. B. 1956 Rotating fluids. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies). Cambridge University Press.
Stewartson, K. 1952 On the slow motion of a sphere along the axis of a rotating fluid. Proc. Camb. Phil. Soc. 48, 168.Google Scholar
Stewartson, K. 1958 On the motion of a sphere along the axis of a rotating fluid. Quart. J. Mech. Appl. Math. 11, 39.Google Scholar
Stewartson, K. 1968 On inviscid flow of a rotating fluid past an axially-symmetric body using Oseen's equations. Quart. J. Mech. Appl. Math. 21, 353.Google Scholar
Taylor, G. I. 1917 Motion of solids in fluids when the flow is not irrotational. Proc. Roy. Soc. Lond. A 93, 99.Google Scholar
Taylor, G. I. 1922 The motion of a sphere in a rotating liquid. Proc. Roy. Soc. Lond. A 102, 180.Google Scholar
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. Roy. Soc. Lond. A 104, 213.Google Scholar