Skip to main content
    • Aa
    • Aa

On the mechanisms of icicle evolution


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.

Corresponding author
Email address for correspondence:
Linked references
Hide All

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 20 *
Loading metrics...

Abstract views

Total abstract views: 81 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th May 2017. This data will be updated every 24 hours.