THE DEVELOPMENT OF THE THEORY OF TURBULENCE AND NONLINEAR DINAMICS (1940—1990)
Dobrov Institute for Scientific and Technological Potential and Science History Studies of the NAS of Ukraine
Nauka naukozn. 2021, 2(111): 137-153
Section: Science and technology history
Abstract: Recently, the concept of turbulence has gone beyond the natural sciences and is widely used in social sciences, economics, world politics, history of science and technology. Turbulent processes are the processes of self-organization of a large system of particles into stable dissipative structures of physical, biological, social, economic nature. Therefore, it is very important and relevant to carry out a more complete than before analysis of the evolution of the concept of turbulence and methods of its study.
The purpose of study is to present the history of discoveries in the theory of turbulence, which have influenced the formation of nonlinear dynamics. The research was performed using methods of logical analysis, generalization, classification, and systematization. The historicalscientific method was used to evaluate the scientific results of scientists.
The article considers the contribution of A.M. Kolmogorov to development of the theory of turbulence; emerging of the theory of turbulence of Landau — Hopf (1944—1948) and its influence on the formation of concepts, ideas and models of nonlinear dynamics. The shift to the turbulence of Landau-Hopf influenced on the inception of the theory of turbulent flows (the theory of Ruelle — Takens, 1971). The difference between these theories have been established. The article discusses the further development of turbulence research in the 60—80s of the twentieth century; the study of plasma turbulence (there appear highly nonlinear problems) — in particular, the study of isolated waves in plasma (N. Zabuski and M. Kruskal, 1965), the theory of Feigenbaum (1978—1979), the theory of turbulent motion of Pomeau — Manneville (1980). It is concluded that the theory of turbulence of A.M. Kolmogorov (1941), the origin and development of the theory of Landau — Hopf (1944—1948) and the theory of Ruelle — Takens (1971), and also the further studies of turbulence influenced on the formation of nonlinear dynamics and its concepts (formation of the concept of a strange attractor, a constructive concept of self-similarity).
It is concluded that the development of the theory of turbulence influenced the formation of nonlinear dynamics of its concepts (the concept of a strange attractor, the constructive concept of self-similarity). In 1971, D. Ruel and F. Tuckens, criticizing the Landau — Hopf theory, were the first to point to the existence of a strange attractor that demonstrates sensitivity to initial conditions (the strange attractor — one of the basic concepts of nonlinear dynamics).
The research of J. McLaughlin and P. Martin (1974) and J. Gollab and H. Swinney (1975) also contributed to the formation of the concept of a strange attractor and the development of the Ruel — Takens turbulence. Based on the turbulence of Landau — Hopf, in clarifying the question of how turbulence arose, in 1978, G.M. Zaslavsky proposed a simpler model of a strange attractor, which establishes a connection between two types of chaotic motion. In 1983, V.S. Afrai novich and L.P. Shilnikov introduced the concept of quasi-attractors.
In 1996, the Ukrainian scientist A.N. Sharkovsky proposed the concept of “ideal turbulence” — a new mathematical phenomenon in deterministic systems.
The theory of turbulence is developing rapidly in Ukraine and abroad, gradually spreading to various fields of science and technology.
Keywords: turbulence, nonlinear dynamics, dynamical systems, attractor.
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