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Nature of Turbulence

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The Essence of Turbulence as a Physical Phenomenon

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Abstract

The main dispute about the origins and nature of turbulence involves a number of aspects and issues in the frame of the dichotomy of deterministic versus random. In science this dispute covers an enormous spectrum of themes such as philosophy of science, mathematics, physics and the other natural sciences. Fortunately, we do not have to venture into this ocean of debate and opposing and intermediate opinions. This is mainly because (as it now stands) turbulence is described by the NSE which are purely deterministic equations with extremely complex behavior enforcing use of statistical methods, but this does not mean that the nature of such systems is statistical in any/some sense as frequently claimed. The bottom line is that turbulence is only apparently random: the apparently random behavior of turbulence is a manifestation of properties of a purely deterministic law of nature in our case adequately described by NSE. An important point is that this complex behavior does not make this law either probabilistic or indeterminate.

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Notes

  1. 1.

    Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ”old one.” I, at any rate, am convinced that He does not throw dice (Einstein 1926).

    Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can’t be seen (Hawking and Penrose 1996).

    Today “chaotic” and “deterministic” are not considered as counterparts of a false dichotomy. This takes its origin to Poincare (1952), H. Poincare, Science and hypothesis, pp. xxiii–iv, Dover, 1952.

  2. 2.

    However, we repeat that since Leray (1934) until recently one was not sure about the theoretical, but not observational, possibility that turbulence is a manifestation of breakdown of the Navier–Stokes equations. Also note the statement by Ladyzhenskaya (1969): ... it is hardly possible to explain the transition from laminar to turbulent flows within the framework of the classical Navier-Stokes theory.

  3. 3.

    The en masse comes from the analogy with statistical physics. But there one has literally many similar objects - molecules. So one realization there may well suffice either, see below.

  4. 4.

    The basic question (which usually is not asked) concerning statistical description is whether such complex behavior permits a closed representation that is simple enough to be tractable and insightful but powerful enough to be faithful to the essential dynamics. Kraichnan and Chen (1989).

    The problem is that in such an approach the rotational and dissipative aspects are not considered as belonging to the essential dynamics.

  5. 5.

    The experimental evidence points to the opposite: the microstructure is not statistically independent of and even not decorrelated from the energy containing eddies, see below, Chaps. 7 and 8 below and Chap. 6 in Tsinober (2009) and references therein.

  6. 6.

    We mention that formally there exist two closed formulations which in reality are suspect to be just a formal restatement of the Navier Stokes equations, at least, as concerns the results obtained to date. One is due to Keller and Fridman (1925) infinite chain of equations for the moments and the equivalent to this chain the equation by Hopf (1952) in term’s of functional integrals.

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Authors and Affiliations

  1. School of Mechanical Engineering, Tel Aviv University, Tel Aviv, Israel

    Arkady Tsinober

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  1. Arkady Tsinober
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Tsinober, A. (2019). Nature of Turbulence. In: The Essence of Turbulence as a Physical Phenomenon. Springer, Cham. https://doi.org/10.1007/978-3-319-99531-1_5

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  • DOI: https://doi.org/10.1007/978-3-319-99531-1_5

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