Geological Fluid Mechanics – Class Summary for 10.18.2013

A bunch of people didn’t show up for class this day, but we had a good discussion without them. After telling stories about Sir Taylor, we talked about the non-uniqueness of the Saffman-Taylor instability solution in relation to the Darcy flow uniqueness theorem. The statement of the uniqueness theorem that we read states that the Darcian flow field has a unique solution when buoyancy forces are not involved and the flow field is divergence free. We concluded that the finger interface in the S-T problem makes possible a discontinuity in the flow velocity across that interface, which violates that divergence-free assumption of the uniqueness theorem.

Then we talked about the Holtzman et al. paper for a while, specifically their scaling law formulations. One thing that the paper didn’t make clear is the origin of their “capillary entry pressure” function, which depends on the pre scale disorder (the lambda term) in such a way that it goes to infinite when lambda goes to 1. This doesn’t seem like such a great model, but we decided that a good deal of explanation probably is included in longer paper published by the authors in Physical Review E.