SIAM News Blog

Studying Frazil-ice Dynamics with Population Models

By Karthika Swamy Cohen

Growth of frazil or granular ice contributes significantly to ice formation in the cryosphere. It is a rapid mode of ice formation, occurring as the initial phase of ice expansion in turbulent waters. It is initiated from supercooled water on the ocean surface. When water is cooled efficiently by the atmosphere and reaches below freezing temperatures—a condition that can arise in gaps in the ice pack and extensive areas of open water—frazil ice accumulates as a suspension of crystals in oceans, lakes, rivers, and sub-glacial ice streams. 

Frazil ice also develops under floating ice shelves as fresh, buoyant “ice shelf water” flows beneath ice shelves. The significant variation in freezing temperature of seawater in this region (due to differences in pressure) causes the temperature of the floating plume to fall beneath freezing temperatures resulting in frazil ice creation.  

Better understanding of microphysical processes that influence the conversion of water to ice-crystals below freezing temperatures show that these ice crystals grow faster than previously understood. 

At the SIAM Conference on Mathematics of Planet Earth, being held this week in Philadelphia, Pa., David Rees Jones described continuum models of a population of ice crystals to provide better comprehension of the treatment of frazil ice in large-scale models.

The Drygalski Ice Tongue, a floating glacier in the Victoria Land coastal ocean region, exhibits a very rapid rate of ice formation.

To set the stage, Jones showed a picture of the Drygalski Ice Tongue, a roughly 80 km long floating glacier in the Victoria Land coastal ocean region of the Western Ross Sea, which exhibits a very rapid rate of ice formation. Here, as sea ice is pushed away from the shore, near freezing point water temperatures generate more ice. Ice crystals pile up along the edge of a polynya, and long streaks of ice crystals form.

Frazil ice is a mass of ice crystals formed in a turbulent flow in a supercooled condition. Disc shaped crystals form in suspension beneath the surface. 

Jones studies the process of frazil ice formation to get insight into how these microscale processes affect larger scale processes. 

The climate model he uses comes from population dynamics and studies a population of ice crystals in a range of sizes. The continuum model analyzes the evolution of the crystal size distribution and crystal growth rate. 

When water is cooled efficiently by the atmosphere and reaches below freezing temperatures, frazil ice accumulates as a suspension of crystals in open water.

The function of crystal growth is studied in conjunction with other physical processes that influence frazil ice dynamics. Jones and his colleagues apply the model to a simple mixed layer, i.e., the ocean surface, and to a floating plume under a surface ice shelf.

Jones presented numerical calculations and scaling arguments for the prediction of frazil-ice explosions, which he demonstrated are aided by faster crystal growth, higher secondary nucleation, and slower gravitational removal. These explosions are affected by crystal growth rate since it changes the size distribution of crystals and also modifies the transient evolution of frazil ice. This promotes a rapid rise in frazil concentration.

Continuum models of ice crystal populations allowed the team to identify steady-state crystal size distributions, which while generally unaffected by crystal growth rate. They are, however, influenced by the relative importance of secondary nucleation to gravitational removal. This indicates that crystal size measurement could be used to estimate the nucleation rate indirectly. Jones also showed that frazil-ice dynamics significantly affects plumes underneath ice shelves. 

Karthika Swamy Cohen is the managing editor ofSIAM News.


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