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Reynolds Equation and Mixing Length Model
PHENOMENOLOGICAL MODELS FOR TURBULENCE
Reynolds Equation
Since turbulence is a continuum phenomenon, the instantaneous velocity and
pressure fields satisfy the Navier-Stokes equation. i.e.,
 ,
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(1)
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 ,
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(2)
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During a turbulent motion  and
p are random functions of space and time. Hence, these may be decomposed into mean and fluctuating parts, i.e.
where  and
 are the mean quantities and
 and p' are the
fluctuating parts. Here, a bar on the top of the letter stands for the (time) averaged quantity. That is
 .
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(5)
| From the table and the schematic diagram, it is observed that
for  ,
 and a turbulent flow cannot exist.
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,
,
,
,
,
,