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The Quarterly Journal of Mechanics and Applied Mathematics 1958 11(1):39-51; doi:10.1093/qjmam/11.1.39
© 1958 by Oxford University Press
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ON THE MOTION OF A SPHERE ALONG THE AXIS OF A ROTATING FLUID

K. STEWARTSON

( Department of Mathematics, The University Bristol )

The motion of a sphere along the axis of an unbounded fluid rotating with uniform angular velocity is discussed on the assumption that the fluid is undisturbed far upstream. It is shown that no wave-like components can then occur upstream of the body. The stream function {psi} and the drag are found for various values of the Rossby number ka, defined in (1. 1) below. When ka = 5·76 both these quantities become infinite everywhere and it is inferred that the fluid cannot be undisturbed far upstream when ka ≥ 5· 76. It is probable that cylindrical flow which must then be present must also occur at smaller values of ka of which the lower bound is not known.


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