Assumptions About The Mixing Length
From the figure above, we can see that the size of a turbulent eddy near the surface is constrained by its proximity to the surface; turbulent eddies centered near the surface cannot be as large as those centered further from the surface. From this consideration, it is reasonable to assume that the mixing length, is proportional to the eddy's depth in the surface:
,
where is the depth and is known as the von Kármán constant. Thus the gradient can be integrated to solve for :
.
So we see that the mean flow in the surface layer has a logarithmic relationship with depth.
Read more about this topic: Surface Layer
Famous quotes containing the words assumptions, mixing and/or length:
“All of the assumptions once made about a parent’s role have been undercut by the specialists. The psychiatric specialists, the psychological specialists, the educational specialists, all have mystified child development. They have fostered the idea that understanding children and promoting their intellectual well-being is too complex for mothers and requires the intervention of experts.”
—Elaine Heffner (20th century)
“It was not till the middle of the second dance, when, from some pauses in the movement wherein they all seemed to look up, I fancied I could distinguish an elevation of spirit different from that which is the cause or the effect of simple jollity.—In a word, I thought I beheld Religion mixing in the dance.”
—Laurence Sterne (1713–1768)
“At length they all to merry London came,
To merry London, my most kindly nurse,
That to me gave this life’s first native source;
Though from another place I take my name,
An house of ancient fame.”
—Edmund Spenser (1552?–1599)