Manchester Applied Mathematics and Numerical Analysis Seminars

Spring 1999

April 21, 1999, 2.30 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

Flow-induced morphological instability of a mushy layer with application to sea ice

Dr. Daniel Feltham, Dept. of Chemical Engineering, UMIST

A mushy region is a mixture of solid and liquid phases coexisting in thermodynamic equilibrium, for example dendrites bathed in their own melt. The essential physics of mushy layer formation from binary alloys (such as sodium-chloride in water solution) is described and a continuum model describing local conservation of heat and solute is presented. This model is then applied to a layer of sea ice (the mush) at the surface of the polar ocean (the melt). A forced flow-induced instability of a mush--melt interface due to Bernoulli-suction is described which relies on the fact that mushy layers are porous. This is illustrated using a linear stability analysis using the mushy layer model with Euler flow in the melt and Darcy flow in the mush. Drawbacks of this analysis motivates the use of the Navier-Stokes equations in the melt, and more involved calculations which are presented in outline. The results of the analysis are then applied to sea ice and discussed.

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