Anisotropic Thermal Conductivity Model for Dry Snow

Abstract

Fabric tensors quantify the directional arrangement of a granular material's microstructure. In treating snow as such they are beneficial in characterizing morphologies that exhibit a distinct directional arrangement—like chains of grains in depth hoar and potentially other weak layers. Microstructural variables, including the directional arrangement of bonds, impact thermo-mechanical properties like strength, stiffness, and conductivity of the granular material. The conductivity model proposed here incorporates a fabric tensor, linking the textural arrangement of a granular assembly to a material property. In this work, dry dense snow was subject to temperature gradients (100 and 50 K/m) in a lab. The resulting morphology was driven by temperature gradient metamorphism. Underpinning the importance of microstructure, the observed heat transfer coefficient (EHC) increased in the direction of the applied gradient without appreciable changes in density. Periodic tomography yielded measurable microstructural data used to calculate a fabric tensor and the evolving conductivity tensor. Through the fabric tensor the analytical conduction model accounts for ~ 43% of the observed increase in EHC. The model also calculates a decrease in conductivity in the plane orthogonal to the temperature gradient due to a developing anisotropy. Snow metamorphism models parameterized by density alone cannot predict such directionally-dependent behavior because they are strictly valid for only isotropic materials.