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Fig. 5. The effect of vector subtraction on streamlines. No subtraction (F): this
presents the measured data free from any manipulations, therefore the frame of
reference is fixed with respect to the thorax and laboratory. Free stream
subtraction 0° (A): here the velocity due to the windtunnel flow has been
subtracted from the measured velocity vectors so that the frame of reference
is fixed with respect to a distant particle in the flow, far enough away to be
unaffected by the moth. These two cases represent the simplest manipulation of
the data and transform the vector fields between two equally valid frames of
reference - fixed with respect to the thorax of the moth, and fixed with
respect to the distant fluid. However, it is not entirely clear that either of
these two global frames of reference will be locally appropriate for resolving
the LEV formed by a flapping wing. For flows that occur close to the surface
of the animal, a locally valid frame of reference might be expected to take
into account the local geometry of the body - so for, example, where the
freestream is deflected as it flows around the body it would make sense, when
looking for features in that flow, to subtract the freestream modified by its
deflection around the body. Vorticity is unaffected by such frame of reference
corrections, but now the frame of reference is a somewhat abstract concept -
being fixed relative to distant fluid flowing with the freestream once it has
been deflected by the body, but unaffected by the flow induced by the flapping
wings. In the case shown here, a deflection of between 10° and 20° the
frame of reference is adequate to see the streamlines converge to a focus
coinciding with the peak in vorticity. The focus shifts from left to right
during the iterations and then disappears altogether as it is transformed into
a form only visible as a shear region.
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