A Brown University/Rhode Island School of Design Dual-Degree student (BRDD, 2017), artist, writer, scientist, and explorer of the world dedicated to finding Wondrous things. Art, design, science, literature and the connections between them. For my original artwork see http://arianamakesart.tumblr.com/
The Navier-Stokes equation fully describes the flow of a fluid. It is essentially an application of Newton’s second law (that a force acting on a body is equal to its rate of change of momentum) to a fluid. Obviously, a fluid is much harder to model than a single solid body with a given mass and velocity. Instead, the fluid is given a density ρ and a velocity vector field, v(x, y, z, t), which describes the speed and direction of flow at the point (x, y, z) and at a time t.
The left-hand side of the equation then is essentially the ‘mass times acceleration’ part of Newton’s second law, and the right-hand side is the total force - in this case, the sum of a pressure gradient, a stress divergence and an external force.
This equation will fully describe the mixing of milk and tea as well as the dynamics of hurricanes.
Unfortunately though, in almost all circumstances it is impossible to solve or even compute to a high level of accuracy! In fact, one of the Clay Institute’s $1m prizes awaits anyone who can gain a great deal of insight into Navier-Stokes existence and behaviour.
However, the amazing thing about this equation is that it tells us (in theory) everything we need to know about the flow of a fluid. The complex behaviour of a rushing river or a swirling vortex is all locked up in these five simple(ish) terms.