Unformatted text preview: to Eqs. (6.7), and take the time mean of each equation. The continuity relation reduces to
u
x y w
z 0 (6.13) which is no different from a laminar continuity relation.
However, each component of the momentum equation (6.7b), after time averaging,
will contain mean values plus three mean products, or correlations, of fluctuating velocities. The most important of these is the momentum relation in the mainstream, or
x, direction, which takes the form
du
dt p
x
y gx
u
y x
u u
x u z 2 u
z (6.14)
uw  v v u 2,
u , and
u w are called turbulent stresses
The three correlation terms
because they have the same dimensions and occur right alongside the newtonian (laminar) stress terms ( u/ x), etc. Actually, they are convective acceleration terms (which
is why the density appears), not stresses, but they have the mathematical effect of stress
and are so termed almost universally in the literature.
The turbulent stresses are unknown a priori and must be related by experiment to  eText Main Menu  Textbook Table of C...
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 Spring '08
 Sakar
 Fluid Dynamics, eText Main Menu, Osborne Reynolds

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