Turbulence: the Equation Nobody Can Solve: Navier-Stokes, Million-Dollar Millennium Prize Problem, and Hidden Mathematics of Everything That Flows

We can land a probe on a comet. We cannot prove that the equation for a glass of water always has an answer. The equations that describe every moving fluid on Earth were finished in the 1840s. They govern blood in an artery, air over a wing, weather, ocean currents, the cream in your coffee. They fit on a single line. Nobody knows whether their solutions are always well behaved. In three dimensions the best available answer dates from 1934 and has stood unimproved ever since. It is not a solution in any sense the discoverer wanted, and he said so himself, at length, in the same paper. Thirty-two chapters. No equations to work through. One page carries an equation, and it is there to be looked at, not solved. - Why a fluid without friction produces a result so absurd it embarrassed the field for a century - The motionless layer of air sitting on every wing, and why it changes everything - A thread of dye in a Manchester laboratory, and the single number that judges every flow - Why nobody can say exactly when smooth flow breaks up - Perfectly determined and completely unpredictable at the same time - What would even count as an answer, and why that question took a century to sharpen - The seven problems announced in Paris in 2000, and why one of them is about water - The speed that becomes infinite, and why proving it cannot happen is so hard - The flat world where all of this works perfectly, and why our world does not - How engineers get answers anyway, priced in core-hours and calibrated guessing - Why a forecast stops being a forecast after ten days, and not a day more - The wake behind a jumbo jet, and the two minutes that matter - Dimples, seams and spin, and where turbulence is deliberately manufactured Including the cases where it went wrong. An airliner that came apart behind another aircraft's wake. A crash with nothing on the radar. What stirring actually does, the sound inside a narrowed artery, and why a cold shower behaves the way it does. This is the story of the last great unsolved problem in classical physics, the one that governs almost everything you can see moving, written for people who want to understand what the difficulty actually is rather than be told that it is difficult. Scroll up and start reading.