Onset of Glacier Tables

A glacier table consists of a rock supported by a slender column of ice and form naturally on glaciers. We investigate the onset of their formation at a smaller scale in a controlled environment. Depending on the size and thermal conductivity of a cap, it can either form of a table standing on an ice foot, or sink into the ice block. A one-dimension conduction model shows that the differential ice melting is controlled by a competition between two effects: a geometrical amplification, and a heat flux reduction due to the higher temperature of the cap as compared to the ice. Our model captures the transition between the two regimes and identifies a dimensionless number which controls the onset of glacier tables formation.

Figure 1

(a) Picture of a glacier table taken in June 2019 on the Mer de Glace in the French Alps. The table diameter is about 1 m. (b) Artificial glacier table made of extruded polystyrene (XPS), 10 h after being put on a flat ice surface.

Figure 2

Heat flux $q_{\text{total}}$ received by an ice plate inclined with an angle $\theta$ with respect to the horizontal (a) as a function of the distance $x$ from the leading edge and (b) as a function of $x/\sin \theta$. Graph (c) shows $q-q_{\mathrm{ray}}$ as a function of $x/\sin \theta$. The black lines correspond to the expressions of $q_{\text{total}}$ (b) and $q_{\mathrm{conv}}$ (c) given in Eq. (1) with an adjustable numerical prefactor $A=0.61$.

Figure 3

Cylindrical caps with aspect ratio $\beta =1/2$ made of XPS, PVC, and granite, in the initial state (a), after 4 h (b) and 8 h (c). The red arrows denote the initial vertical positions of the top of the caps. The green dashed line corresponds to the initial position of the ice surface.

Figure 4

Vertical position of caps (red solid markers) and of the air-ice interface (blue empty markers, see [26]) as a function of time for caps made of (a) XPS, (b) PVC, and (c) granite with an aspect ratio $\beta =1/2$ and radius $R=42$, 41, and 31 mm respectively.

Figure 5

Ratio $v_{\mathrm{cap}}/v_{\mathrm{ice}}$ as a function of the dimensionless number $h_{\mathrm{eff}}R/\lambda$ for three values of the aspect ratio $\beta =H/(2R)$. The solid black lines correspond to Eq. (2) with $\eta =2.5$.