<DOC>
<DOCNO>
255
</DOCNO>
<TITLE>
an approximate solution of the turbulent boundary layer
equations in incompressible and compressible .
</TITLE>
<AUTHOR>
lilley,g.m.
</AUTHOR>
<BIBLIO>
coa r134, 1960.
</BIBLIO>
<TEXT>
  if over the 'outer region' of the boundary layer, where the mean
velocity varies but little from its value outside the shear layer, a
virtual eddy viscosity is defined, which is constant over the outer
region but varies in the direction of the mainstream, a solution of the
turbulent boundary layer equations can be found which satisfies the
appropriate boundary conditions .  the solution leads to a compatibility
condition for the virtual eddy viscosity in terms of the wall shear
stress, the boundary layer momentum thickness and the mainstream
velocity, at least for the case of a constant external velocity .  this
compatibility condition, which can be expressed as
for moderate to high reynolds numbers, where is the shear velocity,
is the boundary layer thickness and is the virtual eddy (kinematic)
viscosity, is just the condition townsend (1956) found for the
equilibrium of the large eddies .  the numerical value of the constant
derived by townsend agrees with ours for reynolds numbers (based on x)
of about .  with this relation for an equation, analoguous to the
momentum integral equation solution, can be found for as a function of
local freestream velocity, with one disposable parameter .
</TEXT>
</DOC>
