Successive stages and the role of natural vortex dislocations in three-dimensional wake transition

Abstract

The time-history of the development of the three-dimensional transition features in a nominally two-dimensional flow configuration is established for Reynolds number 220 in a cylinder wake. The identification of the successive stages that evolve very fast during experiments is possible by means of direct numerical simulation. The physical processes related to the creation of streamwise and vertical vorticity components and their impact on the spanwise waviness of the main von Kármán vortex filaments are analysed by means of the Craik–Leibovich shearing instability mechanism and a comparative discussion is given with respect to the elliptic stability theory. This study proves the existence of a further stage in the three-dimensional transition, which substantially modifies the regular spanwise undulation. This is a systematic and repetitive development of natural vortex dislocations in the near wake. The definition of this kind of structure is provided, as well as its properties related to a drastic reduction of the fundamental frequency and to the selection of a lower path in the Strouhal–Reynolds number relation. The induced amplitude modulation of the flow properties along the span is also evaluated. Quantification of these properties is carried out by using wavelet analysis and autoregressive modelling of the time series. The reasons for the development of natural vortex dislocations are analysed and related to specific modulations of the spanwise structure of the longitudinal velocity upstream separation. From this part of the study an optimum shape for the spanwise distribution of this component can be specified, able to trigger the vortex dislocations in wake flows and therefore useful to apply in the context of stability theory analyses and in further DNS studies.