### The discovery of elastic turbulence shows more similarities to classical Newtonian turbulence than expected.

Blood, lymph fluid and other biological fluids often exhibit unexpected and sometimes confusing properties. Many of these biological substances are non-Newtonian fluids, defined by their nonlinear response to stress and strain. This means that non-Newtonian fluids do not always behave in the manner typical of fluids. For example, these unique liquids can change shape under light pressure while acting almost like solids under more intense force.

Biological solutions are no exception when it comes to their unique properties, one of which is elastic turbulence. A term describing the chaotic movement of liquids resulting from the addition of polymers in small concentrations to aqueous liquids. This type of turbulence only exists in non-Newtonian fluids.

Its counterpart is classical turbulence, which occurs in Newtonian fluids, for example in a river when water flows at high speed past a bridge pier. Although mathematical theories exist to describe and predict classical turbulence, elastic turbulence still awaits such tools despite its importance for biological samples and industrial applications. “This phenomenon is important in microfluidics, for example when mixing small amounts of polymer solutions, which can be difficult. “They don’t mix well because of the strong fluid flow,” explains Professor Marco Edoardo Rosti, head of the Unit for Complex Fluids and Flows.

## New perspectives on elastic turbulence

Until now, scientists considered that elastic turbulence is completely different from classical turbulence, but the latest publication of the Laboratory in the journal Natural communications could change this view. OIST researchers worked in collaboration with scientists from TIFR in India and NORDITA in Sweden to discover that elastic turbulence has more in common with classical Newtonian turbulence than previously thought.

“Our results show that elastic turbulence exhibits a universal power-law decay of energy and previously unknown periodic behavior. These results allow us to approach the problem of elastic turbulence from a new angle,” explains Professor Rosti. When describing flow, scientists often use the velocity field. “We can observe the distribution of velocity fluctuations to make statistical predictions of flow,” explains Dr. Rahul K. Singh, first author of the publication.

When studying classical Newtonian turbulence, researchers measure the velocity throughout the flow and use the difference between the two points to create a velocity difference field. “Here we measure the speed in three points and calculate the second differences. First, the difference is calculated by subtracting the fluid velocities measured at two different points. Then we subtract two of these first differences again, which gives us the second difference,” explains Dr. Singh.

This type of research comes with an additional challenge: running these complex simulations requires the power of advanced supercomputers. “Our simulations sometimes last four months and generate a huge amount of data,” explains Professor Rosti. This additional level of detail led to a surprising discovery: the velocity field in elastic turbulence is discontinuous. To illustrate what intermittent flow looks like, Dr. Singh uses an electrocardiogram (ECG) as an example.

“When measuring an EKG, the signal has small fluctuations punctuated by very sharp peaks. This sudden, large burst is called a burst,” explains Dr. Singh. In classical fluids, such fluctuations between small and very large values have already been described, but only for turbulence occurring at high flow rates. The researchers were surprised to find that the same pattern of elastic turbulence appeared at very low flow rates. “At these low velocities, we did not expect to find such strong fluctuations in the velocity signal,” emphasizes Dr. Singh.

Their findings not only represent a major step toward a better understanding of the physics behind low-speed turbulence, but also lay the foundation for the development of a comprehensive mathematical theory describing elastic turbulence. “With a perfect theory, we could predict flow and design devices that could change the mixing of fluids. This could be useful when working with biological solutions,” explains Professor Rosti.