A continuum mixture theory with an application to turbulent snow, air flows and sedimentation

Abstract

A continuum mixture theory is specialized for the case of turbulent snow, air transport and sedimentation. To facilitate closure a constitutive assumption is made for the turbulent variables of the snow phase in terms of the mean velocities or shear gradients of the airflow. The resulting turbulent equations of motion for the snow phase contain a set of terms which could be characterized as apparent or turbulent buoyancies. The magnitude of these terms is large where shear gradients of the airflow are large. The system of non-linear partial differential equations resulting from the turbulent equations of motion are approximated by finite difference techniques. Solutions for the snow phase velocity and density fields are investigated for a variety of one and two dimensional airflow regimes. The model snow phase velocity and density field solutions are compared with observed snow and air mixture flows over flat surfaces and over the crest of a triangular barrier. Lastly, the accumulation rate of deposited snow on the immediate lee of the two dimensional barrier is compared with observation.