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Problems
5.4.1 Motion of a Vortex Pair Above Ground
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Consider to counter-rotating vortices of strength ±Г, such as trailing the wings of an aircraft. Let the z-axis be the meridian plane and the x-axis be the ground, Fig. 5.11.
The two vortices are initially located at (a, b) and (-a, b). Show, by using images of the vortices below the ground, that the trajectory of the vortices is described by
1 1 _ 1 1
x2 + z2 a2 + b2
Show that the pair of vortices does not hit the ground, but gets as close as zmin = c = ab/J a2 + b2.
Show also that, far from the ground, the vortex pair moves parallel to the z-axis with velocity w = —Г/(4пс).
