Scaling Laws for Melting Ice Avalanches

This Letter describes an investigation of interfacial melting in ice-bearing granular flows. It is proposed that energy associated with granular collisions causes melting at an ice particle’s surface, which can thus occur at temperatures well below freezing. A laboratory experiment has been designed that allows quantification of this process and its effect on the dynamics of a granular shear flow of ice spheres. This experiment employs a rotating drum, half filled with ice particles, situated in a temperature controlled laboratory. Capillary forces between the wetted melted particle surfaces lead to the clumping of particles and enhanced flow speeds, in turn leading to further melting. Dimensional analysis defines a parameter space for further experimentation.

Figure 1

Schematic diagram of a rotating drum experiment investigating avalanching melting ice. (i) Front view; (ii) Cross-sectional side view.

Figure 2

Ice particles in a drum rotating at 3.75 s per revolution with a 47% fill fraction at $-4°\mathrm{C}$.

Figure 3

Velocity (quivers, scaled by a factor of 2) and vorticity map (background color, positive anticlockwise) from the particle image velocimetry analysis of granular ice avalanches in a rotating drum at $-4°\mathrm{C}$. Velocities shown are in the laboratory frame of reference.

Figure 4

Velocity scale ratio for experiments carried out at ${\Theta }_a=-4°\mathrm{C}$ (○), $-2°\mathrm{C}$ (*), $-1°\mathrm{C}$ (□), and $0°\mathrm{C}$ (◃). A linear best fit line has been found with a root mean square residual of 8.7%. Error bars show a single standard deviation confidence interval of 4.8%.

Figure 5

Scaled maximum shear layer velocity versus time for experiments carried out at ${\Theta }_a=-4°\mathrm{C}$, $-2°\mathrm{C}$, $-1°\mathrm{C}$, and $0°\mathrm{C}$. A best fit line has been found, described by Eq. (6), with a root mean square residual of 6.1%. Error bars show a single standard deviation confidence interval of 6.1%.