Self-similarity of trailing vortices

Abstract

Trailing vortices have been repeatedly shown to exhibit a remarkably robust self-similarity independent of the Reynolds number and upstream boundary conditions. The collapse of the inner-scaled circulation profiles of a trailing vortex has even been previously demonstrated for the cases of highly unsteady and turbulent vortex systems, as well as for vortices which were incompletely developed. A number of factors which contribute to and may artificially promote this self-similarity are discussed. It is shown that the amplitude of vortex “wandering” (or the random modulations in the vortex trajectory) observed in some experimental measurements are of sufficient amplitude to cause any arbitrary finite and axisymmetric flow structure to collapse with an idealized trailing vortex when scaled on inner parameters. It is further shown that, for the case of an incompletely developed wing-tip vortex, similarity in the outer core region may be an artefact of the rate of roll-up of the vortex sheet. Great care must, therefore, be taken when interpreting experimental measurements of vortex flows.