<DOC>
<DOCNO>
660
</DOCNO>
<TITLE>
the fundamental solution for small steady three dimensional
disturbances to a two dimensional parallel shear flow .
</TITLE>
<AUTHOR>
lighthill,m.j.
</AUTHOR>
<BIBLIO>
j. fluid mech. 3, 1957, 113.
</BIBLIO>
<TEXT>
  after a brief review of methods of calculating the flow
fields produced by disturbances in rotational basic flows,
the author points out a fundamental difficulty in the
treated as a perturbation of the disturbance field that
would occur if the basic flow were uniform) ..  slow attenuation
of the secondary-flow disturbance with distance
from the obstacle .  the author conjectured (same j. 1
the trouble was caused by nonuniform validity of the
approximation sequence in the region far from the obstacle
.  the analogy with /stokes' and whitehead's
paradoxes/ is mentioned, and a solution analogous to
oseen's is suggested, one in which disturbances, but not
the shear, are assumed to be small .  in this paper, such a
solution is found, and is shown to overlap with the smallshear,
secondary-flow solution .  the basic flow is a parallel,
steady, inviscid, two-dimensional shear flow .  the /fundamental
solution/ due to a weak source is sought .
  the method of fourier transforms is used .  simple solutions
are found for a uniformly sheared basic flow (where
the result coincides with the secondary-flow solution) and
for an exponential basic-flow profile .  in the general case
it is assumed that the parallel basic flow becomes uniform
at, where the x-axis lies in the flow direction .
the character of the solution is determined by studying
its hankel transform, especially for the class of flows
where the total variation of the basic stream speed v(y)
is small .  an interpretation in terms of images, due to
m. b. glauert, is given, and finally the relationship of the
present work to theories of the displacement of the
stagnation streamline (displacement effect of pitot
tubes) is discussed .
</TEXT>
</DOC>
