Experimental investigation of the scaling of vortex wandering in turbulent surroundings

Abstract

The wandering of a wing-tip vortex in free-stream turbulence was documented by analysis of multi-probe hot-wire measurements in a wind tunnel and flow visualisation and particle image velocimetry measurements in a water tunnel. An error-minimisation approach was applied to the hot-wire measurements to estimate the time history of the location of the vortex axis, whereas flow visualisation from two orthogonal views permitted the reconstruction of relatively long sections of the vortex axis. The amplitude of the wandering motion was found to scale with the turbulence intensity, the core radius and the vortex turnover time; this amplitude was insensitive to changes in the integral length and time scales of the turbulence. The period of the vortex wandering was distributed in the range between 1 and 10 vortex turnover times. The wavelength of wandering was distributed at a relatively long value, which scaled with the vortex turnover time. The velocity of vortex wandering depended on the vortex turnover time, but also contained an additional contribution that was consistent with motion induced by bending waves. The prevalence of the vortex turnover time as the scale for vortex wandering was interpreted as evidence that vortex-induced straining of the free-stream eddies bounds the interaction time between the two, thus limiting the time available for linear and angular momentum transfer.