In the final year of my undergraduate degree I was required to do 2 mathematical investigation projects.
The first of these was investigating convection in deep sea black smokers. Here the water seeps into the porous rock of the sea bed and propagates downward collecting minerals along the way. When it returns to the surface and is released in black smoker vents these minerals are what causes the black smoke like appearance at these vents.
In the project I investigated this convection process, the physical process driving it and deriving the governing equations. I then proceeded to do stability analysis of the solutions to these governing equations. I then discussed the adaptation of the basic convection model I had derived and reviewed the literature where high resolution three dimensional models had been used to investigate these.
In the second project I involved investigating and modelling tropical hurricanes.
I again started by deriving the governing equations which drive these hurricanes. After this I used these equations to build a model of the simplified equations to investigate various aspects, such as how changing sea surface temperatures affect the intensity of these hurricanes.