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There are several unreasonable assumptions in the formulation of the Prandlt Mixing Theory. However, it works reasonably well for simple 1-D flow. An attempt to explain why is given by Davidson in his book 'Turbulence', on page 122 - 124, section 4.1.4.

It's stated that it still works because the mixing length theory is really just an extension of vortex dynamics. How? Actually there are two specific questions:

1) In the case of a planar x-y flow, the

2) We might define the vorticity as:

ω

where ū

ω

where u is a typical measure of u' (fluctuating velocity) and l is typical size of the large eddies? I don't understand the physical meaning of this last statement, particularly since in (1) it seems like we said that the fluctuating component of the velocity is relatively insignificant? Why should the vorticity then be defined on the scale of these fluctuating velocities?

Thanks

It's stated that it still works because the mixing length theory is really just an extension of vortex dynamics. How? Actually there are two specific questions:

1) In the case of a planar x-y flow, the

*mean vorticity*(that of the mean flow) points in the z-direction, while that of the*turbulent vorticity*(that of the fluctuating flow) is random. How does this mean that the vorticity of the large eddies is the same order of magnitude as that of the mean flow? Doesn't that assume that the fluctuating velocity is relatively insignificant?2) We might define the vorticity as:

ω

_{z}~ ∂ū_{x}/∂y,where ū

_{x}is the mean velocity. How then, can we extend this to say that:ω

_{z}~ ∂ū_{x}/∂y ~ u/l,where u is a typical measure of u' (fluctuating velocity) and l is typical size of the large eddies? I don't understand the physical meaning of this last statement, particularly since in (1) it seems like we said that the fluctuating component of the velocity is relatively insignificant? Why should the vorticity then be defined on the scale of these fluctuating velocities?

Thanks

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