Hints of elegance in the physics governing snowfall

Most snowflakes do not resemble the intricate symmetrical structures shown in photography books. Some bring to mind frozen pellets; others look like amorphous blobs or contorted crystals. For atmospheric scientists, snowflake morphology helps determine how the flakes descend through the turbulent atmosphere. Now, using a custom-made snowflake-tracking apparatus installed at a ski resort, Tim Garrett, Eric Pardyjak, and Dhiraj Singh at the University of Utah have amassed a unique data set of the shapes, masses, and accelerations of a half-million flakes. Their analysis hints at an unexpected simplicity in the physics that underlies the motion of solid precipitation.

Previously the Utah research team had relied on digital photography to capture the shape and near-surface motion of snow. But understanding how snowflakes respond to turbulence requires knowing other properties, such as density. So the researchers supplemented their setup with a textbook-thick sheet of laser light to aid in particle tracking and an IR camera they developed that was pointed at an aluminum hot plate. Because of the difference in thermal emissivity between aluminum and water, snowflakes striking the plate appeared as white blotches amid a black background, allowing for the determination of the flakes’ geometries. Heat-transfer measurements taken as the flakes melted and evaporated enabled estimates of mass.

The researchers operated the system at Utah’s Alta Ski Area during 10 snowstorms, which allowed them to zap and vaporize snowflakes of many shapes and sizes that fell under various atmospheric conditions. Then they calculated the individual flakes’ vertical accelerations in the laser-light sheet. The results revealed many types of motions: Some flakes, particularly low-density, fluffy ones, got stuck in atmospheric eddies; some got thrust downward at up to 142 m/s², or about 14 times the acceleration of gravity. Yet when the researchers plotted the average accelerations for all 533 000 flakes—encompassing large and small, symmetric and warped, moving through calm air and moving through turbulent air—there emerged a clear-cut exponential distribution, centered on an acceleration of zero.

In a separate analysis, Garrett and colleagues calculated the individual flakes’ expected terminal velocity, a property that depends on the shapes and densities of the flakes but is independent of the conditions in the atmosphere through which they fall. A plot of the fluctuations of those velocities with time also yielded an exponential distribution, one with the same slope as that seen for the accelerations in turbulent air. “Either it’s an amazing coincidence, or it’s hiding some deeper significance,” says Raymond Shaw, an atmospheric scientist at Michigan Technological University.

Garrett and his team next plan to analyze the snowflakes’ measured velocities, which should help clarify the role of turbulence in the flakes’ descent. Many climate models and storm forecasts calculate the terminal velocities of solid precipitation by factoring in only gravity and atmospheric drag. The current and future findings could spur modelers to reassess those assumptions and perhaps lead atmospheric scientists toward a more complete understanding of the behavior of precipitating particles from cloud to surface. (D. K. Singh, E. R. Pardyjak, T. J. Garrett, Phys. Fluids 35, 123336, 2023 .)