Kanpur, May 12, 2023: A team of researchers from the Indian Institute of Technology Kanpur has proposed a universal mechanism for turbulent relaxation, which can be applied to a wide range of fluids, including plasmas and complex fluids. This principle, called the principle of vanishing nonlinear transfer (PVNLT), explains how a turbulent system attains a steady, stable state of relaxation when the driving force is switched off. The study “Universal turbulent relaxation of fluids and plasmas by the principle of vanishing nonlinear transfers” has been published in Physical Review E (Letters) journal. The team comprises Prof. Supratik Banerjee, and researchers Arijit Halder, and Nandita Pan, from the Department of Physics, IIT Kanpur.

To illustrate this concept, the researchers use the example of mixing milk in a cup of coffee. “When we stir the coffee, we create eddies and turbulence that cause the milk to mix quickly. However, when we stop stirring, the system organizes itself via "turbulent relaxation" before it finally ceases to flow. According to PVNLT, this happens when the system gets rid of its nonlinear transfers, terminating the turbulent cascade. In this state, stability is ascertained as a scale-dependent entropy function is maximized when the correlation between different parts of the fluid tends to vanish,” says Prof. Supratik Banerjee.

The PVNLT principle has been shown to give the correct pressure-balanced relaxed states for both two and three-dimensional fluids and plasmas, as previously obtained in numerical simulations. This means the current principle can correctly predict the way the turbulent relaxation happens in reality. This technique is fundamental and can easily be applied to complex fluids, including compressible fluids, plasmas, binary fluids etc.

"Through the principle of vanishing nonlinear transfer, we have been able to uncover a universal mechanism for understanding how turbulent systems reach a relaxed and stable state. Our research has important implications not only for the study of fluids, but also for plasmas and other complex fluids. We are excited about the potential for future applications of this principle in a wide range of fields,” adds Prof. Banerjee.

This research has important implications for our understanding of cosmological plasmas. Cosmological plasmas are plasmas that exist in outer space, such as in stellar envelopes, gaseous nebulae, and interstellar space. Plasmas are a state of matter that consists of charged particles, such as ions and electrons that interact with electromagnetic fields. These plasmas are often dilute, meaning they are not very dense, but they are still important because they play a crucial role in shaping the universe.

One of the interesting features of these cosmological plasmas is that they often exhibit regular patterns, such as "force-free" magnetic fields with a clear alignment between the magnetic field lines and the current. This alignment, popularly called a Beltrami-Taylor alignment, is important because it helps to explain the behavior of these plasmas in outer space. For example, it can explain why some regions of space appear brighter than others in certain wavelengths of light.

However, until now, the mechanism of plasmas obtaining a relaxed state has been a matter of long-standing debate. The research on PVNLT has important implications for our understanding of the cosmological plasmas because it provides a new way of thinking about how turbulent systems, such as plasmas, reach a stable, relaxed state. By understanding how these systems relax, we can better understand their behavior and the patterns they exhibit.

The PVNLT principle provides a unified framework for understanding how turbulent systems reach a stable, relaxed state, from a cup of coffee to the cosmological plasmas. The research has the potential to open up new avenues of study and discovery in both laboratory and astrophysical plasmas.

Reference:

Banerjee, S., Halder, A., & Pan, N. (2023). Universal turbulent relaxation of fluids and plasmas by the principle of vanishing nonlinear transfers. Physical Review E, 107, L043201. https://doi.org/10.1103/PhysRevE.107.L043201

About IIT Kanpur:

Indian Institute of Technology (IIT) Kanpur was established on 2nd November 1959 by an Act of Parliament. The institute has a sprawling campus spread over 1055 acres with large pool of academic and research resources spanning across 19 departments, 22 centres, and 3 Interdisciplinary programs in engineering, science, design, humanities, and management disciplines with 540 full-time faculty members and approximately 9000 students. In addition to formal undergraduate and postgraduate courses, the institute has been active in research and development in areas of value to both industry and government.

For more information, visit www.iitk.ac.in.