Finger Rafting: A Generic Instability of Floating Elastic Sheets

Colliding ice floes are often observed to form a series of interlocking fingers. We show that this striking phenomenon is not a result of some peculiar property of ice but rather a general and robust mechanical phenomenon reproducible in the laboratory with other floating materials. We determine the theoretical relationship between the width of the resulting fingers and the material’s mechanical properties and present experimental results along with field observations to support the theory. The generality of this “finger rafting” suggests that analogous processes may be responsible for creating the large-scale structures observed at the boundaries between Earth’s convergent tectonic plates.

Figure 1

The finger rafting of thin sea ice in the Amundsen Sea. Photograph courtesy of Wilford F. Weeks [22].

Figure 2

Plan view of finger rafting as observed in thin wax sheets of thickness in the range $170–380\mu \mathrm{m}$. The width of the field of view here is around 30 cm and the white line highlights the edge of the fingered wax sheets.

Figure 3

Plan view of two floes A and B colliding. (i) A small protrusion in floe A leads to an overlap of the floes in a small region, C. (ii) This overlap causes oscillations in the vertical position of the floes, which decay away from C. The sign of these displacements is indicated by the $+/-$ symbols in the figure. Notice that the oscillations along the free edge are exactly out of phase in the two floes causing the two floes to alternately ride over and under each other under compression (arrows).

Figure 4

Wavelength of the fingering pattern, $\lambda$, for floating sheets with differing characteristic length scales, ${\ell }_{*}$. The data plotted here are a combination of those in ice (obtained from the field observations of others) and our own experiments with thin sheets of wax floating on water (denoted by ×). The solid line shows the theoretical prediction (8).