Stokes introduced us to the fluid world of Fluid Mechanics and how Fluids move. However, my relationship with Gabriel Stokes is divine. It was during a lecture on his work that I could showcase my understanding of Physics.
Career Shaping Work of Stokes
I recall an event regarding this equation that shaped my professional career; it goes something like this. I attended a History of Mathematics conference in March 2004 at Oxford University. There was an eminent speaker, Ivan Grattan Guinness (1941-14), giving a talk on the Navier-Stokes equation.
During his talk, it occurred to me that he had mentioned everyone important in its development except the person I thought was fundamental (in this case, Newton). During the Q&A, I mentioned to him that the most important protagonist had been omitted. He replied to me, “Who was that?”. I asked him, “Before I answer, I will ask you what this equation means?”. To which he was a bit flummoxed and just pointed at it. I said no, those are just symbols.
I explained to him that the left-hand side contained the acceleration following the fluid. The right-hand side contained the forces (viscous and the stress tensor) and the inclusion of the density term (mass). So it was a rewrite of Newton’s 2nd law of motion. Well, the then Director of Studies of Mathematics was also in attendance. During the coffee break, he sought me out for a chat two weeks later; an interview was set up, and the rest is history.
Navier-Stokes Fluid Mechanics Equation
So, after all that, one can see that the equation is Newton’s mass acceleration formula F = mdv / dt and not F = d(mv)/dt, which would be used in relativity. Stokes himself follows a long line of “Giants” in the prestigious position of Lucasian Professor of Mathematics. This is, arguably, the most famous chair in all Mathematics, including the likes of Newton, Airy, Babbage, Dirac, and Lighthill.
Returning to George, his work on fluid motion and viscosity led to his calculating the terminal velocity for a sphere falling in a viscous medium. I was fortunate to derive his law at UCL during my lectures on dimensional analysis. George also derived an expression for the drag force exerted on spherical objects with very small Reynolds numbers. He also has a beautiful integral formula named in his honor. The formula relates the normal component of the curl of a vector to the circulation comparable to the beauty in Gauss’ divergence theorem.
The Team keeps on Growing
I have not mentioned the other half of the tag team, i.e., Claude Louis Henri Navier (1785-36). He was taught Mathematics by the “Giant” J.Fourier (1768-30) whilst at the École Polytechnique. I have a friend at Oxford who tells me that he attended lectures by Dirac when he was at Trinity College. However, he mentions that he was not inspiring at all. This echoes the reports on Newton often, and he gave lectures to an empty class due to being such an appalling teacher. Navier can be found with his name “up in lights” on the Eiffel Tower, but that discussion is for another day.
