Professor Keith Moffatt, University of CambridgeListen Now Download as mp3 from the show The Seven Million Dollar Maths Mystery A leading Millenium Prize Problem is the NavierStokes equation, which, if solved, could model the flow of any fluid  that means how airplanes navigate the skies, how water meanders in a river and how the flow of blood courses through your blood vessels... Understanding these equations in more detail will lead to scientific advances in all of these fields: better aircraft design, improved flood defences, and better drug delivery in the body. Fluids expert and mathematician Keith Moffatt took Tom Crawford down to the deep dark depths of Cambridge’s maths lab... Tom  We’ve just gone underground and we’re stood outside a lab called the Goldstein Lab. It kind of reminds of a secret lair of either a superhero or maybe a supervillain. There are all kinds of complicated looking devices, cameras everywhere, all kinds of equipment and wires coming out of things. So these equations, the NavierStokes equations, they are a set of mathematical equations that model the flow of any fluid. That could be air, water, even blood in the body perhaps? Keith  Yes, that is correct. For the vast majority of fluids particularly air and water, the equations are based on Newton’s Laws, so they're very classical. They were first written down in the 19th century and they're highly mathematical in structure. Tom  So, if we have these equations that model the flow of all of these different kinds of fluids then why is this a millennium problem? Keith  It is an unsolved problem although many people have tried. There's question of whether solutions of the famous NavierStokes equations can or cannot become infinite. You might say it’s a problem that you might throw the computer at. We’ve got extremely powerful computers nowadays, but a computer can never tell you whether a solution actually is going to infinity. A computer programme will always break down before the singularity is reached. Tom  When I think of singularities, I'm thinking of the Big Bang or a black hole in space. What exactly do you mean by singularity here? Keith  Well, singularity in general means that you have a system of equations in which one of the variables, any one, may go to infinity. Tom  Do we have any examples with fluids that exhibit this singularity behaviour? Keith  The singularity may occur most simply through a consideration of the problem of two tornadolike vortices. If these are forced together, then they go through a process of what's called “Vortex Reconnection”. It’s a very complex process because each vortex tries to wind around the other. The spatial structure becomes very complex. So the question is, can it become infinitely complex. Tom  How close are we to actually understanding this problem? How far away is the solution? Keith  30 years. Tom  I’ll hold you to that. Multimedia
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