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The spin-up from rest of a fluid-filled torus

Published online by Cambridge University Press:  26 April 2006

F. N. Madden  and
T. Mullin
F. N. Madden
Affiliation:
Department of Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Oxford OX1 3PU, UK
T. Mullin
Affiliation:
Department of Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Oxford OX1 3PU, UK
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Abstract

We present the results of an experimental and numerical study of the spin-up from rest to solid-body rotation of a fluid-filled torus. In separate experiments, the rotation rate of the container is suddenly increased to a fixed value and the final rotation rate is used to define a non-dimensionalized control parameter, C. At low values of C, the observed flows during the transient phase are axisymmetric and spin-up is achieved through viscous diffusion. This in turn is followed by significant secondary flow and the appearance of ‘fronts’ as C is increased. During the transient phase the fluid motion near the inner wall of the container is dynamically unstable according to Rayleigh's criterion. Thus at higher values of C wave-like structures break the axisymmetry, non-uniqueness in the details of the process is found and finally, an innear wall instability is observed directly. A plot of the spin-up time versus C shows breaks in the slope at transition points between each of the above dynamical regimes but the overall trend is found to be insensitive to the details of the fluid motion. Further elucidation of the dynamical processes is provided by a novel variant of the now standard phase-space reconstruction techniques. The results show a systematic splitting of the phase paths as C is increased.

Finally, in the complementary numerical study, the time-dependent Navier–Stokes equations are solved for axisymmetric flows. Here, the flow is computed using a velocity–streamfunction–vorticity formulation in a two-dimensional plane with a velocity component normal to this plane. The quantitative and qualitative agreement between the numerical and experimental results is excellent for moderate values of the dynamical control parameter C.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 265 , 25 April 1994 , pp. 217 - 244
Copyright
© 1994 Cambridge University Press

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