Some Basic Laws of Isotropic Turbulent Flow Page: 4 of 37
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NIAk TM No 1.07g 3
of time ,t are deno.ted by ... and yI..,and' their projec-
tions, oh thKaif es by. vij and vi- '. .Th average magnitudes
. . 'ti a , . 7 7 . . ." ( ,1)
are called, following Friedmann and Keller, Wassociation
moments of the second order." .These nine magnitudes con-
stituto a. tensor of the second rank 0, called the tensor
of the association moment, With regard to the averaging
the'usual averaging with respect to 'time of.he turbulence
theory is assumed,. Use is also made of the gQnarally a.ssmod
Equations (3) and (4) are applicable,. as is known,' for the
condition that the avarago functions may be considered as
constant (or slightly. vargring) functions in the averaging
" interval. .
(3) CP . .
t .The tensor - in the general case of a homogeneous
flow depends only on the jre],ative' position of the points N
and MI. that is, on the vector r and on the time, A par-
ticular case is where the association moment tensor is a
function 1of the time and of. the dietanca....r betweenthe
points. M and X' but not of .their relatirt position in
space. The turbulent flow in which the association moment
tensor at a given instan't does not depend on the directidn
in space of the line connecting the two points,' but only on
the distance between them, is called an1iiitng turbulent
flow,* *Ist.'should be particul~arif nate4 tlidt thei br6perty of
isotropy refers t6 the tensor as a whole a.s a physical magni-
tude and not to 14e individual oowaozents, Lwhch depend on
the relative positton of the 1JA' ,hM'.'add the 'ccor,dinate
The general orni'Qf the''assoation.mo'nent ten'ror' in a
homogeneous, isotropic flow is established by means of the
synthetic (physical) definition of the tensor, By the
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Loitsianskii, L. G. Some Basic Laws of Isotropic Turbulent Flow, report, September 1945; (digital.library.unt.edu/ark:/67531/metadc63978/m1/4/: accessed January 24, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.