Experiments on the morphology of icicles

Icicles form when cool water drips from an overhanging support under ambient conditions which are below freezing. Ice growth is controlled by the removal of latent heat, which is transferred into the surrounding air via a thin film of water flowing over the ice surface. We describe laboratory experiments in which icicles were grown under controlled conditions. We used image analysis to probe the evolution of the icicle shape under various conditions. A recent asymptotic theory suggests that, overall, icicles converge to self-similar shapes which are predicted to be attractors. On the other hand, stability theory predicts that the ice-water interface can become unstable to form ripple patterns on the icicle surface. Our experimental results show that the predicted self-similar profile is only found in certain cases, and that icicles can also exhibit unpredicted nonuniformities such as branching near the tip. We find that pure water icicles are more likely to be self-similar than those grown from tap water. Ripples, which are also deviations from the self-similar profile, were observed to climb upward during icicle growth.

Figure 1

(a) An array of icicles hanging from a rooftop on a cold Canadian winter day. (b) Ripples on the surface of a natural icicle.

Figure 2

A schematic of the icicle growing apparatus.

Figure 3

Averaged plots of the dimensionless radius $\rho$ vs. the dimensionless vertical distance $\zeta$ away from the tip for: (a) the five icicles with the smallest values of reduced $\chi {}^2$ from fits to the self-similar theory; (b) the five icicles with the largest values of reduced $\chi {}^2$. The solid (dark) blue curve is the theoretical prediction, the small green (light) circles in the background show the raw data, and the large red circles in the foreground show the averaged data.

Figure 4

The best-fit exponent $\beta$ from fitting icicle profiles to the general power law $r=\alpha z^{\beta }$, plotted against reduced $\chi {}^2$. The dashed line indicates the exponent $\beta =3/4$ expected from the self-similar theory.

Figure 5

Values of reduced chi-square from fitting experimental icicle profiles to the self-similarity theory. (a) Reduced $\chi {}^2$ plotted against ambient temperature for 26 icicles grown at an input flow rate of $2.6\pm 0.3$ g/min. (b) Reduced $\chi {}^2$ plotted against input flow rate for 13 icicles grown at an ambient temperature of $-10\pm 1^{°}$C. (c) Reduced $\chi {}^2$ for 23 distilled water grown icicles and 41 tap water grown icicles; it is evident that distilled water grown icicles are better described by the self-similar shape.

Figure 6

Photographic time-series of two icicles grown under identical conditions except for the purity of the water supplied: (a) distilled water vs. (b) tap water. The times given are the times elapsed since the initiation of the icicle growth.

Figure 7

Some icicle nonuniformities: (a–b) bent, twisted icicles, (c–d) multitipped icicles, (e) time-series photographs of the initiation of a branched icicle grown on a piece of string (time interval: 10 min).

Figure 8

A space-time plot of ripples on a long vertical finger of ice, using the coordinate system shown on the right. The $x$ coordinate of the edge is plotted as a function of the $y$ coordinate and time. The dashed horizontal reference line shows that the ripples moved slightly upward during growth.