# The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers

@article{Kolmogorov1991TheLS, title={The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers}, author={Andrei N. Kolmogorov}, journal={Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences}, year={1991}, volume={434}, pages={13 - 9} }

§1. We shall denote by uα(P) = uα (x1, x2, x3, t), α = 1, 2, 3, the components of velocity at the moment t at the point with rectangular cartesian coordinates x1, x2, x3. In considering the turbulence it is natural to assume the components of the velocity uα (P) at every point P = (x1, x2, x3, t) of the considered domain G of the four-dimensional space (x1, x2, x3, t) are random variables in the sense of the theory of probabilities (cf. for this approach to the problem Millionshtchikov (1939…

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