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On the mechanisms of icicle evolution

Published online by Cambridge University Press:  18 March 2010

JEROME A. NEUFELD ,
RAYMOND E. GOLDSTEIN  and
M. GRAE WORSTER
JEROME A. NEUFELD*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
RAYMOND E. GOLDSTEIN
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
M. GRAE WORSTER
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

We present a study of a cylinder of ice melting in warm air in order to quantify the heat-transfer mechanisms controlling the evolution of its shape, which are inherent in a range of phenomena involving phase change and fluid flow. Motivated by the initial melting at the top of a flat-topped cylinder of ice, we analyse laminar, natural convection above a cooled, finite, horizontal plate (or below a heated, finite, horizontal plate) and show that, to a very good approximation, the partial-differential, boundary-layer equations can be separated with self-similar vertical profiles scaled by the boundary-layer thickness. We find that the horizontal evolution of the boundary-layer thickness is governed by equations describing a steady, viscous gravity current fed by diffusive entrainment, and therefore describe such flows as diffusive gravity currents. We first use the predictions of our model to examine previous experimental results in two dimensions. Our experimental results relating to the melting of ice in air are then compared with predictions based on our analysis of the axisymmetric thermal boundary layer. This comparison confirms the vertical thermal structure and shows that melting is governed in roughly equal measure by heat transfer from the air, the latent heat of condensation of water vapour, and the net radiative heat transfer from the surroundings to the ice.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 647: Dedicated to Professor S. H. Davis on his 70th birthday , 25 March 2010 , pp. 287 - 308
Copyright
Copyright © Cambridge University Press 2010

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References

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Neufeld et al. supplementary material

Movie 1. A sequence of high resolution images, taken every 15 seconds, of a cylinder of ice melting in air with far-field temperature T0 = 21.7 oC and relative humidity RH = 43.0%. The cylindrical top of the ice, analysed in the accompanying paper, has an initial radius of R = 2.7 cm. The movie has been speeded up by a factor of 200.

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