Discussion Synopsis: Monday, 10/28 - Overview of Phase Change.

H.E. Huppert and M.G. Worster. Flows involving phase change. Handbook of Environmental Fluid Dynamics, edited by H.J. Fernando, CRC Press, 2012.

Premise: Authors provide a fairly concise summary of geophysical applications of flows involving phase changes and mathematical treatments of those applications.

· How accessible was the paper?

o Relatively accessible, although the authors do skim over several of the intermediate steps that link equations. In some instances, this made it difficult to follow the derivations. This was especially true in 35.3.3 when the authors discuss continuum modeling of mushy layers.

o The lack of intermediate mathematical steps may be due to the target audience - those in oceanography and fluid dynamics.

· Dimensionless numbers

o Some commented on the lack of refinement in regards to dimensionless quantities, such as the Stefan number or Rayleigh number. Specifically, how the authors state that if the value is “large” a certain motion or other response will occur. In essence, they do not truly quantify the dimensionless regimes and may have been better served by a providing a table that established the range of phenomena (e.g. amount of turbulence when 1<Ra<5, 10<Ra<15, etc.).

o However, it was brought up that mathematicians know that some dimensionless quantities only contribute to a phenomena when they are much greater than one and effectively don’t influence a system when they are much less than one. Therefore, they do provide some context for the state of a system.

· Applicability to personal research

o Some thought of how these equations may be applied to each individual’s research by replacing certain variables, such as salinity, with other variables. In the case of petrology/geochemistry, salinity could be replaced by a geochemical variation in a magma chamber.

· How could the authors have improved the paper?

o By providing more intermediate steps when deriving each equation.

o Including a couple of plots pertaining to some relationships (e.g. the Gibbs-Thomson relationship) to establish what they represent.

o By giving more examples throughout derivations to establish the physical meaning and motivation for each step.

· Main points of paper:

o Math first, ask questions later.

o Freezing is an important process to numerous geophysical applications from a variety of fields.

o Important challenges persist, such as the inherent difficult in modeling natural phenomena owing to the abundance of processes that act at several scales, all of which contribute to the phenomena under consideration.