TY - JOUR
T1 - The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
JF - Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
SP - 9
LP - 13
M3 - 10.1098/rspa.1991.0075
VL - 434
IS - 1890
AU -
A2 -
Y1 - 1991/07/08
UR - http://rspa.royalsocietypublishing.org/content/434/1890/9.abstract
N2 - §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) Denoting by Ᾱ the mathematical expectation of the random variable A we suppose that ῡ2α and (duα /dxβ)2― are finite and bounded in every bounded subdomain of the domain G.
ER -