Investigation of the Stability of the Laminar Boundary Layer Page: 4 of 88
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NACA TN No. 1115
then neutral and self-excited "subsOnic" disturbances exist in the in-
viscid fluid. (The subsonic disturbances die out rapidly with distance
from the solid surface.) The conditions for the existence of other
types of disturbance have not yet been established to this extent of
exactness. A formula has been worked out to give the amplitude ratio of
incoming and reflected sound waves.
It is found in the present investigation that when the solid bounld-
ary is heated, the boundary layer flow is destabilized through the change
in the distribution of the product of density and vorticity, but stabi-
lized through the increase of kinematic viscosity near the solid bound-
ary. When the solid boindary is cooled, the situation is Just the
reverse. The actual extent to which these two effects counteract each
other can only be settled by actual computation or some approximate
estimates of the minimum critical Reynolds number. This question will
be investigated in a subsequent report.
Part III deals with the stability of laminar flows in a perfect gas
with the effect of viscosity included. The method for the numerical
computation of the stability limit is outlined; detailed numerical cal-
culations will be ca rried out in a subsequent report.
INTRODUCTION
In a recent paper (reference 1), one of the present authors has
clarified the theory of the stability of two-dimensional parallel flows
in a homogeneous viscous incompressible fluid. The experimental inves-
tigations of H. L. Dryden, G. B. Schubauer, H. K. Skramstad (reference
2) and H. W. Liepmann (reference 3) agree with the calculations male by
Tollmien (reference 4), Schlichting (reference 5) and those given in the
paper quoted (reference 1). Because of the increasing importance of
phenomena of gas flow at high speeds, it seems natural that the investi-
gation should be extended to cover the case of a gas, taking into ac-
count the effects of compressibility and heat transfer.
The interest in this problem is further eranced by the fact that
disturbances of finite amplitude in high--speed flows are known to have
the tendency of building themselves up into shock waves. It is there-
fore possible that instability of high-speed laminar flows will lead to
shock waves instead of turbulence.1 Although an instability theory in-
volving on.l mall disturbances would not be able to settle this point,
it at least paves the way to such an investigation.
This possibility was first pointed out to the authors by Doctor
H. W. Liepmainn.
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Lees, Lester & Lin, Chia Chiao. Investigation of the Stability of the Laminar Boundary Layer, report, September 1946; (https://digital.library.unt.edu/ark:/67531/metadc55056/m1/4/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.