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Relationship Between Vortex Meander and Ambient Turbulence

Efforts are underway to increase the capacity of airports by use of closely-spaced parallel runways. If achieved safely and efficiently during both visual and instrument flight conditions, it will be necessary to develop more precise methods for the prediction of the motion and spread of the hazard posed by lift-generated vortex-wakes of aircraft. The purpose of the present study is to relate the magnitude of the meandering motion of vortex filaments to the turbulence level in the ambient flow field. The analysis begins with a study of the observations made in the airstreams of the two largest NASA wind tunnels where a small amount of data are available on the magnitude of turbulence-induced vertical and lateral meander of vortices shed by aircraft models. It is found that the turbulence level based on the maximum amplitude of meander is much less than the root-mean-squared value measured in the free-stream of the wind tunnel by use of hot-film anemometers. An analysis of the time-dependent motion of segments of vortex filaments as they interact with an eddy, indicates that the inertia of the filaments and of vortex ovals retards their motion enough in the early part of their travel to account for a large part of the difference in the two determinations of turbulence level. It is concluded that vortices do not move precisely with the fluid elements where they are embedded, but lag behind so that actual meander distances are a fraction of those estimated by the non-slip assumption. Application is then made of the foregoing relationships to meander distances used for the initiation of the long-wave instability, which contributes substantially to wake intrusion distances during landing and takeoff operations at airports. It was found that the best simulation predicts that ovals meander about 58% of the distance predicted without slippage. Because turbulent flow fields are a mixture of eddies rather than a single eddy, a further reduction to the 40% value found in the wind tunnels appears reasonable.