Lift is the force which holds an
aircraft in the air. From a Newtonian perspective, lift is generated
by turning a flow of air. The flow turning
from the wing which can be observed in
The flow turning that occurs in the creation of lift also creates
bound vorticity within the airfoil. For a general shaped
airfoil, there is some distribution of vorticity which we can think
of as small vortices. For the simple Joukowski airfoil, shown in this
figure, there is a single vortex present at the center of the
generating cylinder. The flowfield from this
generating cylinder has been conformally
mapped into the airfoil, but the vorticity has been
The existence of the bound vortex (or vortices) within the airfoil
created an important theoretical problem when it was first proposed.
A static fluid has no vorticity within it; vorticity is zero in
a static fluid.
From the fluid
if a fluid initially has no vorticity
within it, then the net vorticity must remain zero within the domain.
With a bound vortex within the object, there
would then have to be another vortex of opposite strength present
within the flow domain. Then the sum of the two vortices, one
spinning clockwise, the other counter clockwise, would be zero as
required by the conservation laws. Where is the other vortex?
It took some very careful experimental work by Ludwig Prandtl to actually
"catch" the other vortex on film. In his experiment he placed an
airfoil in a tunnel with no flow. He turned the tunnel on
and as the flow began he photographed
the flowfield at the trailing edge of the airfoil. What he saw was a
vortex shed from the trailing edge, spinning opposite to the
predicted bound vortex in the airfoil. The shed vortex was
downstream and eventually mixed out due to
in the air stream.
Without viscosity, the shed vortex would remain with constant
strength and would be carried downstream away from the airfoil. This
is depicted by the vortex at the right of the figure.
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