A phase-changing dry snowpack model

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Abstract
An interacting continua framework is adopted to model a dry snow park, which is viewed as a three-constituent mixture composed of an ice matrix whose pore space is occupied by water vapour and dry air. We focus on the response of a one-dimensional vertical snowpack to changes in pressure and temperature at its surface. The time-scale of the surface forcing is assumed to be much longer than the time-scale for thermal transfers and phase change to take place. The constituents are, therefore, in thermal equilibrium with a common temperatureΤwhich is governed by a single bulk-energy balance. In addition, each constituent satisfies a mass and momentum balance. The constitutive postulates and external prescriptions necessary to close the system of equations are discussed in detail. Non-dimensional variables are then introduced formally to draw out the major balances in the equations and construct a reduced system that accurately models the dominant features in the snowpack. It is shown how the effects of phase change enter the leading-order balance. An iterative procedure is constructed to solve the system. Illustrations for the case of a sinusoidal annual temperature gradient imposed at the surface are presented.

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