Theory of natural convection in snow

Authors:
  • DPD. Powers
    D. Powers
  • KOK. O'NEill
    K. O'NEill
  • SCS. C. Colbeck
    S. C. Colbeck
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Abstract
Buoyancy‐driven flows of air in show are modeled including the effects of phase change and inclination. Phase change between water vapor and ice is important because of latent heat terms in the energy equation. Upper boundaries of the snow are taken as either permeable or impermeable, with temperature or heat flux specified at the lower boundary. When the ratio of thermal to mass diffusivity is greater than 1, phase change intensifies convection. When this ratio is less than 1, phase change damps convection. The effects of permeable top and uniform heat flux bottom boundary conditions on heat transfer are quantified and described as linear functions of Ra/Racr, where Ra is the Rayleigh number and Racr refers to the critical value for the onset of Benard convection. The slope of each function depends only on the thermal boundary condition at the lower boundary. If a snow cover is inclined, Rayleigh convection occurs for any nonzero Rayleigh number. Velocity profiles for flows in inclined layers with permeable tops are derived, and it is found that velocity is proportional to Ra sin Φ, where Φ is the angle of inclination from the horizontal. The numerical results for different boundary conditions compare reasonably well with experimental results from the literature.

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