  The main focus of marine oil spill modelling is often on where the oil will
end up, i.e., on the horizontal transport. However, due to current shear, wind
drag, and the different physical, chemical and biological processes that affect
oil differently on the surface and in the water column, modelling the vertical
distribution of the oil is essential for modelling the horizontal transport.
  In this work, we review and present models for a number of physical processes
that influence the vertical transport of oil, including wave entrainment,
droplet rise, vertical turbulent mixing, and surfacing. We aim to provide
enough detail for the reader to be able to understand and implement the models,
and to provide references to further reading. Mathematical and numerical
details are included, particularly on the advection and diffusion of particles.
We also present and discuss some common numerical pitfalls that may be a bit
subtle, but which can cause significant errors.
