# 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={A. 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… Expand

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#### References

SHOWING 1-2 OF 2 REFERENCES

Statistical theory of turbulenc

- Physics
- Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences
- 1935

Since the time of Osborne Reynolds it has been known that turbulence produces virtual mean stresses which are proportional to the coefficient of correlation between the components of turbulent… Expand

Dokl

- Akad . Nauk SSSR
- 1939