Ice and Fluid Dynamics

Abstract:

We consider convective instability in a deep porous medium cooled from above with a linearised thermal exchange at the upper surface, thus determining the impact of using a Robin boundary condition, in contrast to previous previous studies using a Dirichlet boundary condition. With the linearised surface exchange, the thermal flux out of the porous layer depends linearly on the temperature difference between the effective temperature of a heat sink at the upper boundary and the temperature at the surface of the porous layer. The rate of this exchange is characterised by a dimensionless Biot number, Bi, determined by the effective thermal conductivity of exchange with the heat sink relative to the physical thermal conductivity of the porous layer. For a given temperature difference between the heat sink at the upper boundary and deep in the porous medium, we find that imperfectly cooled layers with finite Biot numbers are more stable to convective instabilities than perfectly cooled layers which have large, effectively infinite Biot numbers. Two regimes of behaviour were determined with contrasting stability behaviour and characteristic scales. When the Biot number is large the near-perfect heat transfer produces small corrections of order 1/Bi to the perfectly conducting behaviour found when the Biot number is infinite. In the insulating limit as the Biot number approaches zero, a different behaviour was found with significantly larger scales for the critical wavelength and depth of convection both scaling proportional to 1/ √ Bi

Abstract:

We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution g(h) from Thorndike et al. into a Fokker-Planck-like conservation law. The steady solution is g(h)=N(q)h(q)e(-h/H), where q and H are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for h≪1, g(h) is controlled by both thermodynamics and mechanics, whereas for h≫1 only mechanics controls g(h). Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness h, from which we predict the observed g(h). The genericity of our approach provides a framework for studying the geophysical-scale structure of the ice pack using methods of broad relevance in statistical mechanics.

Abstract:

The physics of ice crystal growth from the liquid phase, especially in the presence of salt, has received much less attention than the growth of snow crystals from the vapor phase. The growth of so-called frazil ice by solidification of a supercooled aqueous salt solution is consistent with crystal growth in the basal plane being limited by the diffusive removal of the latent heat of solidification from the solid-liquid interface, while being limited by attachment kinetics in the perpendicular direction. This leads to the formation of approximately disk-shaped crystals with a low aspect ratio of thickness compared to radius, because radial growth is much faster than axial growth. We calculate numerically how fast disk-shaped crystals grow in both pure and binary melts, accounting for the comparatively slow axial growth, the effect of dissolved solute in the fluid phase, and the difference in thermal properties between solid and fluid phases. We identify the main physical mechanisms that control crystal growth and show that the diffusive removal of both the latent heat released and the salt rejected at the growing interface are significant. Our calculations demonstrate that certain previous parametrizations, based on scaling arguments, substantially underestimate crystal growth rates by a factor of order 10–100 for low aspect ratio disks, and we provide a parametrization for use in models of ice crystal growth in environmental settings.