Effect of stabilizing forces on turbulence Page: 4 of 12
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N.A.C.A. Technical Memorandum No. 625 3
u' = du and of v' is = v1v + P2v2. Since the sign for v'
fluctuates regularly with that of u' we write
The existence or nonexistence of energy for the further
maintenance of the flow in question now depends on which of the
two energy figures predominates. If the energy output exceeds
the shear stress, the difference is available for upholding the
turbulence, but if the lift performance is greater than the
weight difference, the turbulence must perforce die away. Thus
something is left to maintain the turbulence when
FT' du > F(p v1 + P2v) 2 g ?d, or,
after inserting the value of T' and abbreviating
p( g dp (1)
dy 2 dy
One notable feature is the elimination of the chosen sur-
face F, the mixing distance L and the mean value of verti-
cal speed v' from our inequation (1), so that this interpre-
tation does not reveal anything about these two important
quantities. In addition, it is advisab:l'e to designate the
quotient at the right and. left sides of (1) separately. Making
this nondimeisional quantity = 6:
6 = ---dy, (2)
2p( , du-)
yields turbulence for 0< 1 and strong stability; the turbu-
lence dies out when. *> 1. 0 = 0 denotes that the fluid i-s
homogeneous. Since the derivation of the preceding formulas
is primarily a rough estimate, the experiments undoubtedly call
for some kind of correction factor. But. from the construction
of the formulas it may be inferred that; for instance, what the
relevant quantities are and what qualitative course maybe ex-
pected. An inherently homogeneous warm air stream flows over
an identically cold one; for instance, df/dy may temporarily
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Prandtl, L. Effect of stabilizing forces on turbulence, report, June 1931; (digital.library.unt.edu/ark:/67531/metadc277441/m1/4/: accessed April 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.