Easy to witness but hard to understand, turbulence remains a challenge for modern physics.
If you have watched a disorderly flame for a long time, you might have wondered what is happening inside it. The short answer is turbulence.
Turbulence is ubiquitous in the flows all around us — from the gusts of wind surrounding us and the rivers and streams meandering down a mountain to the smoke rising from a chimney. A turbulent fluid contains vortices, fluids swirling around a centre.
The vortices are of different sizes, and they mix to create vortices of yet another size. “A vortex, being a patch of swirling fluid, leads to a collective motion of the patch,” says Vishal Vasan from ICTS-TIFR, who studies turbulence.
The trajectory of each fluid particle in a turbulent flame is highly chaotic and difficult to predict. So, it would be difficult to track the motion of a small part of the flame with bare eyes.
What confounds physicists studying turbulence is how vortices of different scales of length affect each other. The motion of the smallest to the largest vortices, all interacting with each other, affects the entire flow. There is no way to zoom in on a particular length scale and study it independently of others. Moreover, all the vortices get distributed throughout the flow. “It is the prototypical complex system,” says Vishal.
During a public lecture at ICTS-TIFR in December 2023, physicist David Tong remarked that mysteries about fundamental particles of nature and those about turbulent flows are the other most challenging aspects of physics research in the twenty-first century. Both these frontiers of science require employing powerful computers to calculate physical quantities.
Rishita Das from the Indian Institute of Science, Bengaluru, and her colleagues have developed a tool to study the intricate structures of turbulent flows using fewer computing resources than previously. During a seminar at ICTS in February this year, Rishita explained how physicists describe turbulence using statistics.
Segregating quantities across length scales
The mathematics of turbulence hinges on how physical quantities, like pressure and velocity, change across different length scales depending on the flow’s overall nature and the fluid’s viscosity. Viscosity measures a fluid’s resistance to relative motion between its different layers. For example, honey is more viscous than water.
Historically, physicists have observed that some physical quantities related to turbulent flows are similar across the larger length scales — a metre of an evolving flame — to the microscopic length scales within the flame. This similarity helps them study the statistical properties of these physical quantities, like pressure, velocity, and viscosity.
But, sudden and drastic phenomena can occur within these flows. For example, parts of the flame may get extinguished locally at microscopic scales, a phenomenon called quenching.
Rishita and her colleagues’ studies have helped physicists understand that different mathematical quantities are significant at different length scales. Geometric properties at these length scales are universal across different turbulent flows. However, their magnitudes, or the values they take within the flow, depend on the nature of the flow.
The researchers have demonstrated how regions of intense turbulence within the flow may give rise to sudden phenomena inside a burning flame at the smallest of scales, like quenching parts of the flame. This understanding may help reduce fuel loss in car engines.
Simulating the complete range of scales in a turbulent flow requires calculations that the world’s most powerful supercomputers can take weeks to months, says Rishita. But now, they can reveal the finest-scale motions of turbulence in about one-hundredth of that time.
Moreover, the insights from studying the mathematical framework of one problem, like mixing cough jets in the air, can help solve another problem, like algae swimming in turbulent fluids. “Due to the universal nature of small-scale turbulence, our findings can be applied to more complex flow problems by tuning the parameters,” says Rishita.
Rama Govindarajan from ICTS-TIFR, who also studies turbulence, says that the implications may not immediately help aerospace engineers crank up fuel efficiency.
Physicists’ travails aren’t likely to end soon either. The Navier-Stokes equation that describes fluid flows remains unsolved for turbulent flows.
As David Tong hinted, such studies may be able to show the similarities and differences between turbulence and particle physics. “They are indeed trying to understand the key underlying ideas of turbulence,” says David.
To know more about the exciting prospects, read the following papers by Rishita Das and Sharath S. Girimaji:
- Data-driven model for Lagrangian evolution of velocity gradients in incompressible turbulent flows
- The effect of large-scale forcing on small-scale dynamics of incompressible turbulence
- Revisiting turbulence small-scale behavior using velocity gradient triple decomposition
- Characterization of velocity-gradient dynamics in incompressible turbulence using local streamline geometry
- On the Reynolds number dependence of velocity-gradient structure and dynamics
The author thanks Rishita Das, Vishal Vasan, Rama Govindarajan, and David Tong for discussions, and Debasrija Mondal (Centre for Brain Research, Indian Institute of Science) for help with the illustration.