We formulate a model for the mass exchange between oil at and below the sea
surface. This is a particularly important aspect of modeling oil spills.
Surface and subsurface oil have different chemical and transport
characteristics and lumping them together would compromise the accuracy of the
resulting model. Without observational or computational constraints, it is thus
not possible to quantitatively predict oil spills based upon partial field
observations of surface and/or sub-surface oil. The primary challenge in
capturing the mass exchange is that the principal mechanisms are on the
microscale. This is a serious barrier to developing practical models for oil
spills that are capable of addressing questions regarding the fate of oil at
the large spatio-temporal scales, as demanded by environmental questions. We
use upscaling to propose an environmental-scale model which incorporates the
mass exchange between surface and subsurface oil due to oil droplet dynamics,
buoyancy effects, and sea surface and subsurface mechanics. While the mass
exchange mechanism detailed here is generally applicable to oil transport
models, it addresses the modeling needs of a particular to an oil spill model
[1]. This transport model is designed to capture oil spills at very large
spatio-temporal scales. It accomplishes this goal by specializing to
shallow-water environments, in which depth averaging is a perfectly good
approximation for the flow, while at the same time retaining mass conservation
of oil over the whole oceanic domain.Comment: 18 pages, 6 figure
