Nonequilibrium thermodynamics of temperature gradient metamorphism in snow

Abstract

In the presence of a sufficient temperature gradient, snow evolves from an isotropic network of ice crystals to a transversely isotropic system of depth hoar chains. This morphology is often the weak layer responsible for full depth avalanches. Previous research primarily focused on quantifying the conditions necessary to produce depth hoar. Limited work has been performed to determine the underlying reason for the microstructural changes. Using entropy production rates derived from nonequilibrium thermodynamics, this research shows that depth hoar forms as a result of the snow progressing naturally toward thermal equilibrium. Laboratory experiments were undertaken to examine the evolution of snow microstructure at the macro scale under nonequilibrium thermal conditions. Snow samples with similar initial microstructure were subjected to either a fixed temperature gradient or fixed heat input. The metamorphism for both sets of boundary conditions produced similar depth hoar chains with comparable increases in effective thermal conductivity. Examination of the Gibbs free energy and entropy production rates showed that all metamorphic changes were driven by the system evolving to facilitate equilibrium in the snow or the surroundings. This behavior was dictated by the second law of thermodynamics. An existing numerical model was modified to examine depth hoar formation at the grain scale. Entropy production rate relations were developed for an open system of ice and water vapor. This analysis showed that heat conduction in the bonds had the highest specific entropy production rate, indicating they were the most inefficient part of the snow system. As the metamorphism advanced, the increase in bond size enhanced the conduction pathways through the snow, making the system more efficient at transferring heat. This spontaneous microstructural evolution moved the system and the surroundings toward equilibrium by reducing the local temperature gradients over the bonds and increasing the entropy production rate density. The employment of nonequilibrium thermodynamics determined that the need to reach equilibrium was the underlying force that drives the evolution of snow microstructure. This research also expanded the relevance of nonequilibrium thermodynamics by applying it to a complicated, but well bounded, natural problem.