We are interested in finding the velocity distribution at the wings of an aeroplane. Within the scope of a three‐dimensional linear theory we analyse a model which is formulated as a mixed screen boundary value problem for the Helmholtz equation
$(\Delta + k^{ 2}) \varPhi =0$
in
$\mathbb{R}^{ 3}\backslash \overline{S}$
, where
$\varPhi $
denotes the perturbation velocity potential, induced by the presence of the wings and
$\overline{S} := \overline{L} \cup \overline{W}$
with the projection
$L$
of the wings onto the
$(y_{ 1},y_{ 2})$
‐plane and the wake
$W$
.
Not all Cauchy data are given explicitly on
$L$
, respectively
$W$
. These missing Cauchy data depend on the wing circulation
$\varGamma $
.
$\varGamma $
has to be fixed by the Kutta–Joukovskii condition:
$\nabla \varPhi $
should be finite near the trailing edge
$x_{\rm t}$
of
$L$
. We reduce here this screen problem to an equivalent mixed boundary value problem in
$\mathbb{R}^{ 3}_{ +}$
. The main problem is in both cases the calculation of
$\varGamma $
. In order to find
$\varPhi $
we use the method of matched asymptotics for some small geometrical parameter
$\varepsilon$
and the ansatz
$\varGamma = \varGamma _{ 0} + \varepsilon \varGamma _{ 1} + \cdots $
which makes it possible to split the problem into a sequence of problems for
$\varGamma _{ 0},\varGamma _{ 1}, \ldots\,$
. Concretely, we calculate
$\varGamma _{ 0}$
and
$\varGamma _{ 1}$
explicitly by the demand of vanishing intensity factors of the solutions of the corresponding mixed problems at the borderline between
$L$
and
$W$
. Especially, we point out that
$\varGamma _{ 0}$
can be obtained by solving a two‐dimensional problem for every cross‐section of
$L$
while
$\varGamma _{ 1}$
indicates the interaction of these cross‐sections.
