Testing Turbulence’s Limits

Clouds have some of the largest Reynolds numbers on Earth, thanks to length scales that vary from kilometers to less than a millimeter.

Understanding chaotic, turbulent flows has long challenged scientists and engineers due to their sheer complexity. In turbulent flows, energy cascades from the largest scales — like the kilometer-size cross-section of a cloud — to the very smallest scales, less than a millimeter in size, where viscosity transforms the flow’s motion to heat. For nearly a century, our theoretical understanding of turbulence has posited that there are certain universal behaviors in the statistics of a turbulent flow — essentially that, due to this energy cascade, some aspects of every turbulent flow are the same from clouds to ocean currents to your coffee cup.

Accordingly, experimentalists have tried for decades to measure this expected universality. Often, there are some signs of agreement, and any deviation was attributed to the finite difference between the large and small scales of the flow. (The theory assumes the difference in these scales’ size is effectively infinite.) But now researchers have achieved the largest range of scales yet — comparable to those found in the atmosphere — and the gaps between theory and experiment remain. The new study does show signs of universality but in a different way than existing theory predicts. As the authors point out, we’ll need new theories to explain these findings. (Image credit: D. Páscoa; research credit: C. Küchler et al.; via APS Physics)

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