The motion of the trailing vortices associated with a lifting wing is investigated by theoretical and visual-flow methods for the purpose of determining the proper vortex distribution to be used for downwash calculations. Both subsonic and supersonic speeds are considered in the analysis.It is found that the degree to which the vortices are rolled up depends upon the distance behind the wing and upon the lift coefficient, span loading, and aspect ratio of the wing. While the rolling up of the trailing vortices associated with high-aspectratio wings is of little practical importance, it is shown that, with low-aspect-ratio wings, the trailing vortex sheet may become essentially rolled up into two trailing vortex cores within a chord length of the trailing edge.The downwash fields associated with the two limiting cases of the flat vortex sheet and the fully rolled-up vortices are investigated in detail for both subsonic and supersonic speeds. The intermediate case in which the rolling-up process is only partially completed at the tail position is also discussed.

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A general "sound boundary" curve was developed which establishes the combinations of minimum flow Reynolds numbers and percent stenosis required for the onset of vascular murmurs. The curve was derived by a combination of engineering analysis and animal experiments in which thin circular orifice plates were implanted in the descending aortas of anesthetized dogs. The results indicate that the sounds are produced by jet instability and the associated "free turbulence" in the flow. Such turbulence may occur at Reynolds numbers far below that for transition in a straight pipe, depending upon the degree of stenosis. However, below this critical Reynolds number for any given degree of stenosis, a murmur would not be detected even with perfect hearing or an ideal microphone, since the flow remains steady and the jet (if any) is laminar and silent. In pulsating flow, sounds can be produced only when this critical Reynolds number is exceeded. KEY WORDSstenoses turbulence critical Reynolds number sounds orifice plates flow measurement jet instability dogs