My work on my PhD has all been with inviscid fluids, that is to say that is no shearing, the fluid is free to flow. I have been working on a simple extension to the infinite depth case and I found some interesting results. The method I have been using has been using the visco-potential approach, that is I have been extending the potential approach by decomposing the velocity vector into a gradient and curl part and assuming that the viscosity is small. The initial results look very good, as expected the viscosity adds a single term to my original equation, it is a complex term and this allows for waves.

There has been work to model free surface flows using a Reynolds approximation approach, the analysis was completed with a forcing – topography, so any extension to this analysis would include going up to 3D or adding a surface current, this would involved adding a charge evolution equation.

Waves in viscous electrohydrodynamics