JINR Prizes for 2021

On the phenomena of turbulence in liquids and gases

The series of articles "Calculation of critical exponents and representative physical parameters of the scaling behavior of stochastic systems by quantum field theory methods" was awarded the first JINR prize in 2021 in the category "For Theoretical Physics Research". The series of articles includes papers published by a team of scientists over the past 25 years. The team of authors consists of Loran Adzhemyan, Nikolay Antonov, Michal Hnatic, Juha Honkonen, Polina Kakin, Georgy Kalagov, Mikhail Kompaniets, Tomasz Lucivjansky, Lukasz Mizisin, Mikhail Nalimov, representing BLTP JINR, St Petersburg State University, Pavol Jozef Safarik University and IEP SAV in Kosice (Slovakia), University of Helsinki and National Defense University of Helsinki (Finland). Head of the new Sector of the Bogoliubov Laboratory of Theoretical Physics "Quantum field theory in complex systems", established on his initiative, Professor Michal Hnati? tells about these papers.

Research on turbulent motions in liquids and gases is carried out at the Bogoliubov Laboratory of Theoretical Physics of JINR that helps to learn the laws which a majority of natural phenomena are subordinate to. Making more accurate weather forecasts, calculating the trajectory of industrial emissions and better comprehending numerous other processes is possible using complex equations.

Flows in liquids and gases are of two basic types: turbulent: chaotic, vortex, and laminar: moving in layers, without mixing. If the movements of the second kind are ordered and their trajectory is easy to determine, then in the case of turbulent flows everything is not easy and to predict in what place and what amount of gas or liquid will be produced after a certain period of time, will be possible only approximately. Scientists admit: a complete theory of turbulence is incredibly hard to construct; nevertheless, over the past quarter century, the scientific community has made progress in understanding these processes.

Turbulence describes an entire category of phenomena in the atmosphere and hydrosphere of our planet: winds and sea currents, waves, tornadoes and tsunamis, the drift of garbage patches in the World Ocean, others. Even blood can flow through veins as laminar (usually under conditions of physiological rest) and turbulently - when its viscosity changes, a blood vessel narrows or expands, plaques are produced in an artery or vein.

There are practically no completely laminar flows in nature; they are more common in very viscous liquids. Viscosity provides the flow a "braking force", creates internal friction. The greater the viscosity of the system is, the more energy should be pumped in order to spin motion in it. Such a movement always tends to veer towards turbulence, chaos. Therefore, it is fundamentally impossible to predict the weather exactly, in all details, even with the most modern computers that calculate the direction and speed of air currents. Weather forecasts are most accurate when the weather is calm, as long as the air current is close to laminar one. Then, for instance, we can say that good, warm weather will last five days - in this case, there are almost no mistakes. As soon as sufficiently strong drops in atmospheric pressure arise on the outskirts of the atmospheric front, the air starts to turbulize, "to spin".

Turbulence has a tremendous impact on the transport of various impurities in oceans, seas or in the air, such as, on the spread of smoke from a chimney in a thermal power plant or in a factory. Scientists can track how smoke spreads, but at the same time they give only average characteristics: how big the cloud will be on average after a certain period of time. In this case, the cloud will have a complex shape, but if we imagine it as a kind of average ball, then, for instance, it would have a diameter of three kilometers. We can also determine the average propagation velocity of this cloud.

Such investigations allow to find out what the average concentration of substances will be in a turbulent flow at a certain distance from the pipe. It allows to calculate how far the residential area should be located from the industrial facility and how high the pipe should be so that the smoke does not fall on the city.

Transport of particles is a complex phenomenon. There are various equations that describe the motion of an object in space and time. Many of them describe the trajectory unambiguously, for instance, when shooting from a rifle, aiming from one point, you hit a certain target, aiming a little higher, you hit another one higher. This movement can be controlled. In turbulence, nothing can be controlled - instability occurs, errors accumulate - the so-called butterfly effect appears. There are equations that describe this uncontrollability, yet they allow one to derive only some average characteristics, to estimate the correlations in the system.

Now, let's talk about our team and its activities, awarded the first JINR Prize for 2021. Using the methods of quantum field theory, we have investigated classical turbulence systems, as a result of which we have obtained various novel non-trivial results: the energy spectrum has been calculated and the occurrence of intermittency or fractality has been explained. It has been proven that turbulence as if "flickers": there are islands of laminarity in it that disappear in one place and appear in another one. The alternation of such laminar sections with chaos is called intermittency or fractality (multifractality).

Another striking result is the investigation of the dependence of the rate of chemical reactions in a complex turbulent medium. We have derived complex equations that can be solved and thus predict the dependence of the concentration of chemically reactive particles per unit volume on time. Over time, these particles, colliding, cease to be reactive, produce a chemically inert molecule that no longer participates in the reaction. The precipitation rate of molecules or a decrease in the concentration of these chemically reactive particles depends on the medium in which the process takes place. It is also of great practical significance. Poisonous substances emitted with smoke from the chimney can be neutralized over time. So, the chaotic process helps to accelerate the disappearance of chemically reactive particles.

Turbulence obtained experimentally.

On the basic results of the work

The theoretical description of turbulence is the most significant unsolved problem of classical physics. Of course, the concept of turbulence covers a wide category of physical phenomena of another nature and any exhaustive and definitive "theory of turbulence" can hardly be constructed. However, the canonical list of problems: the occurrence and stability of solutions to hydrodynamic equations, convective turbulence, instability of laminar flows, damped turbulence and others that have significant practical and conceptual significance, is in the focus of attention of theorists. One of them is the problem of describing developed (homogeneous isotropic) hydrodynamic turbulence in the inertial interval.

Turbulent flows occurring in various liquids or gases at very high Reynolds numbers show a range of common properties and phenomena (cascade of energy or other conserved quantities, scaling behavior with apparently universal power-law "anomalous exponents" and others), indicating that the latter can be described within the framework of an internally consistent theory. The most remarkable feature of developed turbulence that does not fit into the framework of the classical phenomenological Kolmogorov-Obukhov theory is intermittency that occurs due to strong fluctuations in the energy dissipation rate and manifests itself in a singular dependence, presumably a power law one, of simultaneous correlation and structure functions on distance, characterized by an infinite number of independent anomalous indicators (multi-scaling). Both experiments and numerical simulations show that anomalous scaling is more pronounced for the passive transport of scalar/vector fields of temperature, impurity density, magnetic field than for the velocity field itself, so the problem of passive transport is an integral part of the research of scaling in a turbulent medium.

A related category of tasks concerns the research of the role of turbulence in fluids near the critical point, at which the system is extremely sensitive to external impacts and hydrodynamic fluctuations that ultimately result in the occurrence of new dynamic scaling classes of universality in both classical and quantum systems, such as, in liquid helium, where the vanishing viscosity automatically results in arbitrarily large Reynolds numbers even at low flow rates.

Fluctuations of a random velocity field, including turbulent ones, affect many other stochastic processes in nature. Among them, chemical reactions occurring in random media feature prominently; models of non-equilibrium critical behavior of Kardar-Parisi-Zang, describing the coarsening of a randomly growing surface; models of directed percolation describing the spread of fire fronts, epidemics, the growth of tumors and bacterial colonies. It turns out that taking into account the turbulent motion of the medium significantly expands the categories of the universal behavior of such systems.

It should be emphasized that the main dynamic quantities (velocity, concentration, magnetic field and others) are random fields and their dynamics is described using nonlinear stochastic equations. The main goal of theoretical research is to find different averaged statistical characteristics of these fields: correlation functions, response functions, structural functions and more complex objects. Appropriate methods to achieve these goals are the methods of quantum field theory - the renormalization group and non-equilibrium statistical physics approaches. The authors have made a great contribution to the adaptation and enhancement of these methods aimed at meeting turbulence problems. New original methods have been developed for calculating the representative constants and parameters of turbulent systems using perturbation theory and calculating the critical dimensions of compound operators that develop the multifractal (intermittent) behavior of the statistical correlations of the random fields under investigation. Since the second half of the 1990s, their use has provided a range of significant results in the theory of developed turbulence and in the research of its impact on other stochastic processes in open systems. The basic results of the paper, including four review articles, were published in top international journals in 1995-2021.

Based on materials published on the website www.jinr.ru