A Discussion of Cone and Flat-Plate Reynolds Numbers for Equal Ratios of the Laminar Shear to the Shear Caused by Small Velocity Fluctuations in a Laminar Boundary Layer Page: 4 of 26
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NACA TN 4078 3
amplification of the disturbance between two boundary-layer Reynolds
numbers on a cone will be A3 if the amplification between the same
boundary-layer Reynolds numbers on a plate is A. This result is the
starting point for the present analysis, the purpose of which is to
investigate the possibility of obtaining a useful approximate relation
between the Reynolds number on a cone and that on a plate for equal
closeness to transition. The analysis is based on the linear stability
theory and on the assumption that the ratio of the shear caused by the
disturbance to the laminar shear is an indication of the closeness to
transition. The information so obtained may be useful if the difference
between the transition Reynolds number and the Reynolds numbers at which
the relations for equal shear ratio become inapplicable is small.
SYMBOLS
A amplification ratio
b ratio of v' to u'
c cr + ici
cr wave velocity of a disturbance of a single frequency
ci amplification parameter; ci < 0 for a decaying disturbance;
ci = 0 for a neutral disturbance; ci > 0 for a growing
disturbance
C1 boundary-layer Reynolds number parameter
7
Cf lam laminar shearing stress coefficient,
2
F( ) function of ( )
k correlation coefficient, UV
M Mach number
r perpendicular distance from point x,y to axis of symmetry
of cone
S amplification parameter
t time
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Tetervin, Neal. A Discussion of Cone and Flat-Plate Reynolds Numbers for Equal Ratios of the Laminar Shear to the Shear Caused by Small Velocity Fluctuations in a Laminar Boundary Layer, report, August 1957; (https://digital.library.unt.edu/ark:/67531/metadc57045/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.