Eduction of large-scale organized structures in a turbulent plane wake

Abstract

Large-scale organized structures in the turbulent plane wake of a circular cylinder are investigated in air up to a downstream distance of 40d at a Reynolds number of Red = 1.3 × 104; d is the cylinder diameter. Velocity signals from a linear transverse rake of 8 X-wires are sampled simultaneously to calculate the instantaneous span wise vorticity. We have appropriately smoothed the temporal traces of vorticity to obtain time evolutions (including the transverse displacement, sign, strength and size distributions) of organized structures identified by vorticity contour maps. The periodicity of the initial structures is rapidly lost: dispersion in streamwise spacing, transverse displacement, strength and size of structures increases with increasing downstream distance.Particular emphasis is placed on examining alternative general schemes for educing coherent structures in natural or unexcited turbulent shear flows, especially in their fully developed states. The optimal eduction scheme employed involves centring the rake at the most probable transverse location of centres of advected structures and accepting those structures that: (i) are centred at the midpoint of the rake, (ii) have a peak value of (smoothed) vorticity of a given sign above a specified level, and (iii) have streamwise and transverse extents of the (smoothed) vorticity contours above a specified size. From successive accepted structure signatures the instants of occurrence of structure centres (i.e. smoothed vorticity peaks) are identified. Un-smoothed signals are then time-aligned with respect to these instants and ensemble averaged to educe coherent structure and incoherent turbulence characteristics. Further enhancement is achieved by iteratively improving the time-alignment by maximizing the cross-correlation of individual structure vorticity with the ensemble-averaged vorticity and by discarding structures that require excessive time shifts or that produce significantly weak peak correlation values.Following this optimal scheme, large-scale coherent structures have been educed in the fully turbulent wake. The average structure centre is found to be closer to the wake centreline than the half-width location, and the structure size does not increase in proportion to the wake width, suggesting that transverse wandering of structures (including their three-dimensionality) increases significantly with increasing downstream distance. The various flow properties associated with coherent and incoherent turbulence, and the coherent structure dynamics, in particular the role of vortex stretching (at the saddle) in turbulence production and mixing, are discussed.