Hypothesis on deterministic turbulence

Abstract

Physical and philosophical aspects of the problem of deterministic turbulence, the idea of which has been suggested by the author about a decade ago and realized later experimentally together with two younger colleagues, are discussed. The hypothesis on the deterministic turbulence is based on a set of philosophical cogitations. In the end, these cogitations resulted in a deduction about the possibility of the principle existence of such a phenomenon as deterministic turbulence. The main part of the sequence of ideas discussed below preceded the first experiments on deterministic turbulence. These ideas were used to formulate the problem and to prepare the experiments. Finally, the correctness of these ideas has been proved and substantiated during subsequent measurements. In contrast to the usual (random) turbulence, the deterministic turbulent flows have reproducible instantaneous structure, representing one particular realization from an infinite number of possible realizations. The author strongly believes that the discovery of deterministic turbulence is a breakthrough in the fields of turbulence, chaos and philosophy. It will be discussed that deterministic turbulence can be regarded as an inherent consequence of the idea on determinism of laws of nature and predictability of real physical systems, even unstable ones. This predictability occurred at least in cases of relatively short intervals of the system development. These features enable reproducibility of the behavior of even very complex real systems having practically an infinite number of degrees of freedom. Such behavior only appears chaotic due to its great complexity, but, simultaneously, can be deterministic, i.e. reproducible, in the essential features, from one realization to another. It is very important to note that deterministic turbulence can exist and can be produced not in all flows. The majority can only be described by usual, stochastic turbulence.