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    Camporeale, Carlo and Ridolfi, Luca 2012. Ice ripple formation at large Reynolds numbers. Journal of Fluid Mechanics, Vol. 694, p. 225.


    Chen, Antony Szu-Han and Morris, Stephen W. 2011. Experiments on the morphology of icicles. Physical Review E, Vol. 83, Issue. 2,


    Chen, Antony Szu-Han and Morris, Stephen W 2013. On the origin and evolution of icicle ripples. New Journal of Physics, Vol. 15, Issue. 10, p. 103012.


    Nakouzi, Elias Goldstein, Raymond E. and Steinbock, Oliver 2015. Do Dissolving Objects Converge to a Universal Shape?. Langmuir, Vol. 31, Issue. 14, p. 4145.


    Cartwright, Julyan H. E. Escribano, Bruno González, Diego L. Sainz-Díaz, C. Ignacio and Tuval, Idan 2013. Brinicles as a Case of Inverse Chemical Gardens. Langmuir, Vol. 29, Issue. 25, p. 7655.


    Bartels-Rausch, Thorsten Bergeron, Vance Cartwright, Julyan H. E. Escribano, Rafael Finney, John L. Grothe, Hinrich Gutiérrez, Pedro J. Haapala, Jari Kuhs, Werner F. Pettersson, Jan B. C. Price, Stephen D. Sainz-Díaz, C. Ignacio Stokes, Debbie J. Strazzulla, Giovanni Thomson, Erik S. Trinks, Hauke and Uras-Aytemiz, Nevin 2012. Ice structures, patterns, and processes: A view across the icefields. Reviews of Modern Physics, Vol. 84, Issue. 2, p. 885.


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  • Journal of Fluid Mechanics, Volume 647
  • March 2010, pp. 287-308

On the mechanisms of icicle evolution

  • JEROME A. NEUFELD (a1), RAYMOND E. GOLDSTEIN (a1) and M. GRAE WORSTER (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112009993910
  • Published online: 01 March 2010
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.

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Copyright
Corresponding author
Email address for correspondence: j.neufeld@damtp.cam.ac.uk
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T. Aihara , Y. Yamada & S. Endo 1972 Free convection along the downward-facing surface of a heated horizontal plate. Intl J. Heat Mass Trans. 15, 25352549.

J. V. Clifton & A. J. Chapman 1969 Natural-convection on a finite-size horizontal plate. Intl J. Heat Mass Trans. 12, 15731584.

A. Dayan , R. Kushnir & A. Ullmann 2002 Laminar free convection underneath a hot horizontal infinite flat strip. Intl J. Heat Mass Trans. 45, 40214031.

W. N. Gill , D. W. Zeh & E. Del Casal 1965 Free convection on a horizontal plate. Zeit. Ang. Math. Phys. 16, 539541.

D. W. Hatfield & D. K. Edwards 1981 Edge and aspect ratio effects on natural convection from the horizontal heated plate facing downwards. Intl J. Heat Mass Trans. 24 (6), 10191024.

H. K. Kuiken 1968 An asymptotic solution for large Prandtl number free convection. J. Engng Math. 2 (2), 355371.

N. Ogawa & Y. Furukawa 2002 Surface instability of icicles. Phys. Rev. E 66, 041202.

H. Schlichting & K. Gersten 2000 Boundary Layer Theory. Springer.

M. B. Short , J. C. Baygents & R. E. Goldstein 2006 A free-boundary theory for the shape of the ideal dripping icicle. Phy. Fluids 18, 083101.

S. N. Singh & R. C. Birkebak 1969 Laminar free convection from a horizontal infinite strip facing downwards. Zeit. Ang. Math. Phys. 20 (4), 454461.

K. Stewartson 1958 On the free convection from a horizontal plate. Zeit. Ang. Math. Phys. 9 (3), 276282.

P. T. Tsilingiris 2008 Thermophysical and transport properties of humid air at temperature range between 0 and 100°C. Energy Convers. Manage. 49, 10981110.

K. Ueno 2003 Pattern formation in crystal growth under parabolic shear flow. Phys. Rev. E 68, 021603.

K. Ueno 2004 Pattern formation in crystal growth under parabolic shear flow. Part 2. Phys. Rev. E 69, 051604.

S. G. Warren 1984 Optical constants of ice from the ultraviolet to the microwave. Appl. Optics 23 (8), 12061225.


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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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