Here we leave this brief introduction to fluid dynamics.We have seen all the principal hydrodynamic interactions that can occur in viscous fluids and begun to understand how they can be modelled mathematically. There are many other physical interactions that occur in fluids. I have mentioned buoyancy but there are also electromagnetic interactions involved in solar physics and the generation of Earth's magnetic field, chemical interactions involved in changing the surface characteristics of fluids and used to help premature babies to cope with the viscous fluid lining of their lungs and enable them to breathe, and fluid–fluid interactions involved in enhancing oil recovery from old wells by pumping in a displacing fluid. These are just a few examples of the many areas of life and science in which fluid dynamics plays a dominant role. And to these, we should add the quest to predict our climate, which involves complex interactions between the two major fluids involved in life on Earth: air and water, our atmosphere and our oceans.

I hope that this course has whetted your appetite to find out more and to consider fluid dynamics an important physical arena in which to utilise your mathematical abilities.