A Turbulent Mixture Theory for the Atmospheric Mixture of Snow and Air

Abstract

A theory based on classical fluid mechanics for an incompressible, chemically non-reacting, atmospheric mixture of air and entrained snow particles is derived. These continuum equations of motion are then expanded to include turbulent flow. The reduced, one-dimensional equations of this theory are further refined by order-of-magnitude analysis and correlation of the turbulent terms to mean flou parameters. The resulting one-dimensional, turbulent equations of motion for the snow contain apparent turbulent forces which enhance entrainment of snow where gradients of the air flow are high. These turbulent equations of motion are then solved numerically for snow particle velocity and concentration as a function of height above the surface. The results are similar to observed profiles of snow concentration and the superposition of the solution of this turbulent mixture theory for snow entrainment with an appropriate solution for the saltation layer will eventually lead to a working continuum theory for blowing snow.