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Reynolds Equation and Mixing Length Model Phenomenological Theories of Turbulence
Prandtl Mixing Length Hypothesis Prandtl argued that
and for a thin shear layer
where
or
G.I. Taylor recovered the mixing length hypothesis based on a vorticity transport formulation and von Karman used a similarity analysis for estimating the mixing length as
The mixing length theory has dominated the field of turbulence modeling for more than half a century. It is now known that the mixing length hypothesis works for turbulent flows, which are characterized by single length and velocity scales. The reason for its effectiveness is simply due to dimensional requirements! |
is the mixing length. Hence,
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