Ripples on Icicles

There is an interesting instability that gives rise to ripples on the surface of icicles. It is believed to be related to a similar process that causes ripples on stalactites in caves, and other ripply patterns on limestone deposits near hotsprings.

In order for ice to form, the latent heat of freezing must be removed. In the case of stalactites, CO2 must come out of solution and be carried away for CaCO3 to form.

In each case, a thin water film flows over a growing surface.  The deposition onto the surface changes its shape, and the shape feeds back onto how the water flows.  The rate of deposition is controlled by how the heat or CO2 is transported through the flowing water and into the surrounding air.

In the end, an icicle or stalactite is unstable to the growth of a "Michelin Man"-like system of ripples.

On icicles, the length scale of the ripples is very nearly 1 cm, and is apparently not strongly dependent on parameters like flow rate or undercooling.

A ripply icicle outside

my dining room window.

A long view of the same icicle from below.

A closer view from below

Videos of icicle ripples

  1. Icicle forming on the outside of a meter stick, mpeg movie by Roger Mong.

  2. Icicle forming on the outside of a round stick, a movie from the cold room at DAMTP.

  3. Another icicle on a round stick.  Ripples are visible at the lower right.

  4. An icicle forming on a bit of wool.

  5. Another icicle growing on a bit of wool

Ripples on a piece of “flowstone” in the Pálvölgyi limestone cave near Budapest.

The main difference between stalactites and icicles is (obviously) that stalactites grow much more slowly, and that the latent heat released by ice formation may lead to buoyancy-driven convection in the air around the icicle. Cave air is probably very still, and not moved by the very slow release of CO2

It is therefore an interesting question how the instability is effected by windy growing conditions.  In general, the air outside an icicle is anything but still.

Cross section of a ripply icicle, showing the traces of the ripple motion in small bubbles. The red line shows ripple motion.

Image courtesy of Norikazu Maeno, Hokkaido University. Fig. 6 from: Maeno & Takahashi, Low Temperature Science, Ser.A43, 125 (1984). [In Japanese].

The scale bar is 13mm long.

Colorized spacetime plot of the edge of an icicle growing on a stick.  Time increases upward. 

Image made by Stephen Morris in the cold room at DAMTP, University of Cambridge.

Do the ripples move?

Symmetry alone suggests that the ripples move, because the water flow breaks the up/down symmetry of the icicle.  Detailed analysis also shows that the linear instability is to traveling waves.

Ogawa and Furukawa’s theory suggests that the ripples move down, while more recent work by Ueno finds upward motion.

The ripple motion can be traced by sectioning icicles and looking at the pattern of small trapped bubbles.

The ripples do appear to go up.

We have directly visualized growing icicles (see videos above) and followed ripple motion using edge detection.

The ripples move upward very slightly (with pauses due to the uneven water flow going elsewhere on the surface).

References and Links

  1. N. Maeno, N. Makkonen, L. Nishimura, K. Kosugi and T, Takahashi, Growth rate of icicles, J. Glaciology, 40, 319 (1994).

  2. N. Ogawa and Y. Furukawa, Surface instability of icicles,  Phys. Rev. E, 66, 041202 (2002). [link].

  3. K. Ueno, Pattern formation in crystal growth under parabolic shear flow, Phys. Rev. E, 68, 021603 (2003). [link].

  4. K. Ueno, Pattern formation in crystal growth under parabolic shear flow II, Phys. Rev. E, 69, 051604 (2004). [link].

  5. Physics News Update Number 613 #2, November 13, 2002. [link].

  6. The research group for phase transition dynamics of ice, at Hokkaido University.

  7. M.B. Short, J.C. Baygents, J.W. Beck, D.A. Stone, R.S. Toomey, and R.E. Goldstein, Stalactite growth as a free boundary problem: A geometric law and its Platonic ideal, Phys. Rev. Lett., 94, 018501 (2005). [link].

  8. M. B. Short, J. C. Baygents, and R. E. Goldstein, A Free-Boundary Theory for the Shape of the Ideal Dripping Icicle,  Physics of Fluids, 18, 083101 (2006) [link].

  9. N. Goldenfeld, P. Y. Chan and J. Veysey, Dynamics of Precipitation Pattern Formation at Geothermal Hot Springs, Phys. Rev. Lett., 96, 0254501 (2006). [link].

  10. Ripply icicles in The Last Word, New Scientist magazine.

The Experimental Nonlinear Physics Group, Dept. of Physics, University of Toronto,

60 St. George St. Toronto, Ontario, Canada, M5S 1A7. Phone (416) 978 - 6810