Dissipation of energy in the locally isotropic turbulence

@article{Kolmogorov1991DissipationOE,
  title={Dissipation of energy in the locally isotropic turbulence},
  author={Andrei N. Kolmogorov},
  journal={Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences},
  year={1991},
  volume={434},
  pages={15 - 17}
}
  • A. Kolmogorov
  • Published 1 April 1941
  • Geology
  • Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
In my note (Kolmogorov 1941a) I defined the notion of local isotropy and introduced the quantities Bdd(r)=[ud(M′)−ud(M)]2,¯[un(M′)−un(M)¯]2, where r denotes the distance between the points M and M', ud(M) and ud(M') are the velocity components in the direction MM'¯¯ at the points Mand M', and un(M) and un(M') are the velocity components at the points M andM' in some direction, perpendicular to MM'. 
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It is found that the moment of the dissipation of kinetic energy of order n is completely determined by 〈(∂u(1)/∂x(1))(2n)〉 and an order- (and viscosity-) dependent coefficient for all n under the assumption of (local) isotropy.
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