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National Advisory Committee for Aeronautics, Technical Notes - Absolute Dimensions of Karman Vortex Motion

Professor Karman succeeded in calculating the resistance
W of a plate, moving perpendicularly to its surface through
water with the velocity U, from data obtained directly from
the phenomenon of the flew.**

Professor {arman investigated the flow for some distance
behind the plate. The experiment showed a regular arrangement
of vortex lines, a "vortex street" (Fig. 2), which, remaining
behind the.p1ate, advanced more slowly than the latter. The
relative dimensions of this arrangement, i.e. the ratio of the
distance 1 between the vortices to the width b of the vor—‘
tcx street (Fig. l), were determined on the basis of a stabil-
ity investigation. The velocity u and a linear dimension
of the vortex system (for instance, the distance 2 between two
successive vortices rotating in the same direction) had to be
found experimentally, in order that the resistance W could
actually be deduced. The question as to the origin of the
vortex system remained unanswered.

According to the law of Helmholtz that no vortex can form
in a frictionless or non—viscous fluid, the viscosity is obvi—
ously responsible for the formation of the vortices.

Considered that an investigation into the phenomena of the bound-
ary layer at the plate would be necessary, in order to calculate
the unknown u and Z of the vortex tail. According to the calf
culations of Oeeen (in. d. Phys. 1915, pp. 231 and 646), We must
nevertheless assume that the influence of viscosity in immediate
proximity to the plate is less than at some distance behind it..
Furthermore, it was shown by Jaffé (P ys. Zeitschr. 1930, p. 541),
that, even in a viscous fluid, in general, no vortex can originate
and that therefore the reason for the formation of vortices ape
pearing everywhere in hydrodynamics cannot be_fcund in the viscos-
ity. According to Jaffé, there is much more cause for the forma—
tion of vortices, when there are discontinuities in the external
forces or in the velocity of the fluid. In the case under con—
sideration

There are certainly such discontinuities present in th
vicinity of the Flats. We will therefore attempt to determine the'
quantities u and 1, respectively % and-fin (d = width of plate.
from a consideration of these discontinuities.