Pattern of inclusions inside rippled icicles

Icicles that have grown from slightly impure water develop ripples around their circumference. The ripples have a near-universal wavelength and are thought to be the result of a morphological instability. Using laboratory-grown icicles and various species of impurities, including fluorescent dye, we show that a certain fraction of the impurities remain trapped inside the icicle, forming inclusions within the ice. The inclusions are organized into chevron patterns aligned with the peaks of the ripples. Within the chevrons, a substructure of crescent-shaped structures is observed. We also examine the crystal grain structure of laboratory icicles with and without impurities. We present the first detailed study of these growth patterns in the interior of icicles and discuss their implications for the mechanism of the ripple-forming instability.

Figure 1

An upward looking view of ripply natural icicles hanging from the edge of a roof.

Figure 2

The extracted topography of icicles with concentrations (a) 0.34 mMol/kg (10 ppm NaCl), (b) 2.7 mMol/kg (80 ppm NaCl), and (c) 22 mMol/kg (640 ppm NaCl). The peaks of ripples are marked by $+$ symbols. Note the different color scales. The arrows in part (c) indicate ripple splitting or stopping events.

Figure 3

Inclusions are visible at a wide range of concentrations in NaCl icicles. At the lowest concentrations [(a) and (b)], the majority of the icicle is pure ice. As the concentration increases, trapped impurities collect in bands that exhibit a chevron pattern [(c)–(e)]. The transitional concentration (f) has thin lines of almost pure ice. At high concentrations (g), the whole of the ice is foggy with inclusions. The blue arrows mark ripple stopping events.

Figure 4

A measurement of the inclusions observed in a section of a 10 ppm NaCl icicle near the root. Downward is to the left. The inclusions vary significantly in size between diameters 20 and 180 $\mu \text{m}$. The crescents features have a typical width of 120 $\mu \text{m}$.

Figure 5

Using sodium fluorescein (a) at the same ionic concentration as used previously for NaCl, we observe that the inclusions glow under UV illumination. The pattern of inclusions qualitatively matches what is observed with (b) NaCl (and other chemical species). Some larger inclusions appear near the central line in (b) that may look like air bubbles, but the corresponding central line in (a) glows with dye. A cross section perpendicular to the icicle axis (c) shows layers of inclusions that resemble the growth rings of a tree.

Figure 6

${\mathrm{Na}}^{+}$ concentrations in the feed water, in runoff water, and in cross sections for a series of NaCl icicles, measured with ICP-OES. The feed water concentration agrees with what is expected from the amount of NaCl added. The runoff water shows only a slightly increased concentration over the feed water. The ratio of concentration in the bulk to that of the feed water, $k$, is nearly constant at $0.27\pm 0.05$ but may increase slightly at higher concentrations. The inset shows this ratio. The dotted line in the inset is the fit $k=0.05{log}_{10}\left(c\right)+0.19$.

Figure 7

An overlay of a cross-sectional image with the edge-detected surface shape taken every 10 rotations shows that the bands of inclusions and crescent shapes closely aligns with the topography. The valleys between the ripples, highlighted in red, match up well with the lines of pure ice seen in the cross section.

Figure 8

Ripple wavelengths of icicles as measured from the (a) topography and (b) cross sections. Gray regions indicate concentrations where ripples are not “well behaved”—not forming at low concentrations or exhibiting uncontrolled dynamics at higher concentrations, when the interior is fully saturated with inclusions. The error bars indicate the standard error of the mean for each wavelength measurement. Sample distributions of individual ripple widths shown for (c) a single edge and (d) one cross section. Both distributions are for icicles with 80 ppm NaCl.

Figure 9

An example of measuring an icicle cross section. The icicle is illuminated with a unidirectional light source to the right. The pure ice that separates bands of impurities are highlighted with lines. The feature widths (green lines) are measured by the distance between each band of inclusions. The distribution of widths can then be used to find the mean and variance of band-to-band distances.

Figure 10

Images of icicle cross sections between crossed polarizers. The upward angle of grains in a rippled icicle (80 ppm NaCl) can be seen in (a), with its corresponding nonpolarized view in (b). When an icicle is grown with a low impurity concentration (20 ppm NaCl) no ripples form (c), and the grains do not exhibit an upward angle. The liquid inclusions are apparent in (d) (40 ppm NaCl), which is also an example of a crystallite spanning multiple ripples. Arrows in (d) point to individual bands of inclusions seen within the single crystallite. The inset (e) shows grains with internal inclusions in an axial cross section.