In the 1960s and 1970s, colorful comic strip advertisements from New York’s Transscience Corporation promised to mail anyone sending cash, a check, or a money order a “bowl full of happiness”—in reality, a small paper envelope containing freeze-dried eggs. Dipped in salt water, the eggs would produce brine shrimp, also known as sea monkeys.
Brine shrimp are about a centimeter long and swim upside down, flapping their legs wildly and dragging their elongated abdomen like a tail behind them. As scientists have recently learned, these tiny swimmers can do much more than just move.
Researchers have long believed that in a turbulent system like a stream of water, energy flows in only one direction, from the largest scales to the smallest, or vice versa, depending on the dimensions of the system. But by observing the humble brine shrimp, scientists at the University of Pittsburgh realized that with just a small adjustment, the flow of energy could be reversed.
Scientists discovered that they could direct the cascade of energy in a two-dimensional system by disrupting the flow of the system with a small obstacle, as long as it was perfectly tilted. “Geometry is important,” said Lei Fang, the Pittsburgh engineer who led the new study.
Artemia are tiny invertebrates that inhabit waters with high salt concentrations. They reach about 10 millimeters long, the width of a pencil eraser.
Nature Image Library/Alamy
The discovery builds on a fundamental, though often overlooked, mathematical description of how forces interact to push energy through a system, said Gregory Falkovich, a physicist at the Weizmann Institute of Science and a pioneer in the study of turbulent two-dimensional systems. “It’s a beautiful and skillful experimental work.”
These findings could extend to larger, more chaotic systems, including those in three dimensions. This work has implications for our understanding of fluid dynamics and could have applications in areas such as pollution control and drug design.
A cascade of chaos
The turbulence is hard to miss. It stirs the harsh foam at the foot of a waterfall and shapes the crest of a breaking wave. It’s behind the bumps of a flight, the swirls of milk in a cup of coffee, and the rolling of plasma on the surface of the sun. “We see turbulence usually everywhere in our lives, when we go to the beach or wash our hands,” said Francesca De Serio, a civil engineer and hydrodynamics expert at the Polytechnic University of Bari in Italy.
A turbulent system is complex, characterized by complex forces and internal disturbances. But it can start simply enough. For example, turbulence occurs when a flowing fluid encounters an obstacle that changes the speed of part of the flow. In a river, the water slows down at the bank due to friction, and differences in speed can produce vortices or whirlpools. When a river splits to go around a rock, speeds change and gaps form; the water falls on itself and can begin to spin. Air is also a fluid, its turbulence produced by competing currents and changing temperatures.
In such a system, energy moves between size scales. The English mathematician and physicist Lewis Fry Richardson, founder of modern weather forecasting, discovered it while studying the fluid systems formed by gases in the atmosphere. He discovered that the kinetic energy of a large eddy fuels smaller and smaller eddies, until it reaches the scale where viscosity, which resists motion, takes over. The energy is ultimately dissipated as heat. In 1922, Richardson expressed the concept in verse:
Large whorls have small whorls
Who feed on their velocity,
And small whorls have smaller whorls
And so on until the viscosity.
Beginning in the early 1940s, Soviet mathematician Andrei Kolmogorov provided a clear and rigorous mathematical basis for the study of turbulence. But his work, like Richardson’s, focused primarily on three-dimensional systems in which energy flows from large elements to smaller ones.
In the late 1960s, physicists Robert Kraichnan and George Batchelor extended their research to two-dimensional systems. Two-dimensional turbulent systems include phenomena like Jupiter’s Great Red Spot, which swirls so violently that it cancels out any movement further into the atmosphere. This type of two-dimensional turbulent system transfers energy from one scale to another, like a three-dimensional system, but with a twist: the energy of a two-dimensional turbulent system cascades in the opposite direction, moving from small eddies to large ones. In Jupiter’s Great Red Spot, smaller vortices and eddies near the perimeter feed the giant maelstrom at the center.
In the decades since these pioneering studies discovered reverse flow in two-dimensional systems, physicists have not questioned in depth whether these flows are fixed. The energetic mechanisms underlying two-dimensional turbulent systems were certainly not on Xinyu Si’s mind around 2021, when he began studying brine shrimp as a student in Fang’s laboratory.
Swimming in the flow of energy
Fang’s lab focuses on “active matter,” a physics term describing objects that move on their own and inject energy into their surroundings. It’s a broad enough label to include networks of living things, like bacteria, and non-living objects, like tiny robots.
In this project, Si and Fang wanted to study how biological swimmers mix materials in fluids where turbulence occurs. The researchers had hypothesized that, in the mixing of fluids in large natural systems, turbulence generated by tiny organisms played an underestimated role. After all, billions of tiny creatures churn the world’s waterways.
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