Adding Viscosity to Free Surface Flows

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

PhD Complete

I am proud to say that I have finally completed my PhD! I have completed my minor corrections and have had them accepted, now all I have to do is hand in the final copy. Here is a copy of my PhD thesis for your interest, constructive comments always welcome.