A Constitutive Theory for Snow as a Continuous Multiphase Mixture

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Department of Civil, Environmental, and Geospatial Engineering; Keweenaw Research Center


Snow on the ground is viewed in this formulation, as a saturated two-phase granular material comprised of small grains of ice with interstitial pores filled by a single vapor. The snow is considered as a continuous mixture in which the ice and vapor constituents are themselves treated as individual but interacting continua.

Mathematical modeling of the Snow is accomplished using a relatively recent continuum theory for mixtures where the individual constituents are physically separate. This approach considers the volume fraction occupied by each constituent as an additional kinematic variable. Therefore, in addition to the balance equations for mass, linear momentum, angular momentum and energy, usually applied in continuum mechanics, an equation which accounts for changes in the volume fraction, called the balance of equilibrated force, is included. Balance equations for each constituent as well as for the mixture are considered. The immiscible nature of the constituents allows constitutive equations to be developed which depend only on those variables which pertain to that constituent. Exchange between the ice and vapor is aecounted for by interaction terms which enter the theory through the balance equations for the constituents. Forms for these interaction terms are used which guarantee that the entropy inequality is not violated.

A one-dimensional analysis of an isothermal homogeneous snow cover suddenly subjected to a colder surface temperature reveals a thermodynamically active zone associated with a large temperature gradient, initially located near the top surface, but which moves downward with time in a wavelike fashion decreasing in intensity. Slight differences in constituent temperatures are calculated during the more active transient phase in conjunction with a decrease in snow density.

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© 1989

Publication Title

International Journal of Multiphase Flow