Approach to local axisymmetry in a turbulent cylinder wake

Abstract

The objective of this experimental study is to characterise the small-scale turbulence in the intermediate wake of a circular cylinder using measured mean-squared velocity gradients. Seven of the twelve terms which feature in e, the mean dissipation rate of the turbulent kinetic energy, were measured throughout the intermediate wake at a Reynolds number of Re d ≈ 3000 based on the cylinder diameter (d). Earlier measurements of the nine major terms of e by Browne et al. (J Fluid Mech 179: 307–326 1987) at a downstream distance (x) of x = 420d and Re d ≈ 1170 are also used. Whilst departures from local isotropy are significant at all locations in the wake, local axisymmetry of the small-scale turbulence with respect to the mean flow direction is first satisfied approximately at x = 40d. The approach towards local axisymmetry is discussed in some detail in the context of the relative values of the mean-squared velocity gradients. The data also indicate that axisymmetry is approximately satisfied by the large scales at x/d ≥ 40, suggesting that the characteristics of the small scales reflect to a major extent those of the large scales. Nevertheless, the far-wake data of Browne et al. (1987) show a discernible departure from axisymmetry for both small and large scales.