Order in Chaos

Although turbulent flow is chaotic, it’s not completely disordered. In fact, order can emerge from turbulence, though exactly how this happens has been a long-enduring mystery. Take the animations above. They show the flow that develops between two plates moving in opposite direction that are separated by a small gap. (The formal name for this is planar Couette flow.) The visualization is taken in a plane at a fixed height between the plates.

Initially (top), the flow shows narrow bands of turbulence, shown in green, separated by calmer, laminar zones in black. As time passes, these areas of laminar and turbulent flow self-organize, eventually forming diagonal stripes that are much longer than the gap between plates (bottom), the natural length-scale we would expect to see in the flow. Researchers have wondered for years why these distinctive stripes form. What sets their spacing, and why are they along diagonals?

To answer those questions, researchers explored the full Navier-Stokes equations, searching for equilibrium solutions that resemble the striped patterns seen in experiments and simulation. And for the first time, they’ve found a mathematical solution that matches. What the work shows is that the pattern emerges naturally from the equations; in fact, given the characteristics of the solution, the researchers found that many disturbances should lead to this result, which explains why the pattern appears so frequently. (Image and research credit: F. Reetz et al., source; via; submitted by Kam-Yung Soh)

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