A Lab Version of Planetary Atmospheres
Atmospheric turbulence encompasses a wide range of flow patterns, from 10-m-wide eddies to 1000-km-long wind streams. Geoscientists want to understand how energy and rotational motion transfer (or “cascade”) from one length scale to another, but atmospheric observations have not provided clear answers. A new model of the atmosphere consisting of fluid in a rotating, meter-wide cylinder is able to reproduce key features of observed turbulence [1]. Using video tracking, researchers mapped out the flow velocity in this system, uncovering the dominant role of a “vorticity” transfer that distributes rotational motion from large vortices into smaller ones. This form of cascade may explain the energy distribution in large-scale turbulence on Earth as well as on other planets.
Turbulence can be characterized by a kinetic energy spectrum, which indicates the amount of energy found in fluctuations at each length scale. The typical turbulence spectrum has a mathematical form called a power law, in which the energy density steadily decreases from large to small scales. Fluid dynamics models of Earth’s atmosphere have predicted that the power law should be relatively flat at large scales (with an exponent of −5/3) and steeper at small scales (with an exponent of −3). However, these predictions aren’t supported by observations. “The basic shape of the spectrum is all wrong,” says Peter Read from the University of Oxford in the UK. Data taken by airplanes have revealed a spectrum that starts out steep at large scales (greater than 500 km) and becomes flatter at small scales.
However, aircraft can only record data along a single line. For a more complete picture, numerical simulations can provide in-depth maps of turbulent flow, but they require making some assumptions. Laboratory models—as developed by Read’s group and others—offer a complementary view of atmospheric turbulence. “We can reproduce much of the same physics on a much smaller scale,” Read says.
The experiment in Read’s lab involves a meter-wide cylindrical tank (with a pipe through the center) filled to a depth of 24 cm with a water–glycerol mixture and rotated at speeds between 0.5 and 10 rpm. The fluid is heated at the bottom near the outer wall—replicating the heating of the atmosphere by sunlight hitting the ground near the equator. At the same time, the fluid is cooled at the top of the tank near the inner wall—reproducing the radiative cooling of the atmosphere at the poles. The resulting convective motion within the fluid is the main energy input that drives the turbulence, explains Oxford team member Shan-Shan Ding.
Compared with previous, similar experiments, Read, Ding, and their colleagues have improved the measurement of the flow velocity, covering a wider range of scales with more precision. They added small particles to the fluid to visualize the motion. Videos of the flow show eddies whose sizes are clearly influenced by changes in the rotation speed and the temperature difference. From the measured particle motion, the researchers computed the energy spectrum, finding a steep drop at large scales (roughly between 5 cm and 5 mm) and a flatter spectrum at smaller scales—consistent with atmospheric observations.
The data set also allowed the team to compute the cascades of both energy and vorticity—a quantity related to the fluid’s angular momentum. The researchers found that energy flowed mainly from small to large scales, but the more significant effect was a transfer of angular momentum in the opposite direction, from large to small vortices. This vorticity cascade, which is predicted in models but usually at small scales, explains the steep energy spectrum that the team observe at large scales.
Read and colleagues found that the strength of this cascade increased as the tank’s rotation rate increased. But they also found that the cascade depended on the temperature difference (or so-called stratification) between the top and bottom layers in the fluid. Models of atmospheric turbulence do not predict this temperature dependence.
The researchers don’t yet have a complete explanation for the observed temperature dependence. But they write that their results could be important for understanding the climate, both on Earth and on other planets. Planetary atmosphere models have to accurately represent the transfers of energy and vorticity, which are fundamental variables in climate dynamics, Read says.
“These experiments produce new insights into how rotation and stratification shape the energy flow across small and large scales in turbulent planetary atmospheres,” says geophysicist Jeffrey Weiss from the University of Colorado Boulder. This energy transfer underlies the formation of jet streams and storms on Earth and other planets. He says that laboratory experiments that reflect Earth’s climate provide a benchmark for complex climate models.
–Michael Schirber
Michael Schirber is a Corresponding Editor for Physics Magazine based in Lyon, France.
References
- S.-S. Ding et al., “Stratification-dependent enstrophy-controlled regime in geostrophic turbulence,” Phys. Rev. Lett. 136, 114101 (2026).