Complete self-preservation along the axis of a circular cylinder far wake

Abstract

Self-preservation (SP) analyses are applied to the mean momentum and the scale-by-scale energy budget equations in the far wake of a circular cylinder. The scale-by-scale SP analysis, which is a two-point analysis, complements the SP analysis of the mean momentum equation. Power-law variations are derived for different length scales (e.g. the Taylor microscale and the Kolmogorov length scale) and velocity scales (e.g. the root mean square and the Kolmogorov velocity scale). Further, the SP solutions for the scale-by-scale energy budget equation are exploited to develop an exact relation to estimate the mean turbulent kinetic energy dissipation rate $\bar{{\it\epsilon}}$ on the wake axis. These SP solutions and the new $\bar{{\it\epsilon}}$ relation are well supported by hot-wire data in the far wake at a Reynolds number of 2000 based on the free stream velocity and the cylinder diameter. On the far-wake axis, both the energy spectra and the structure functions exhibit an almost perfect collapse over all wavenumbers and separations, irrespective of the set of scaling variables used for normalisation. This is consistent with a complete self-preservation (i.e. SP is satisfied at all scales of motion) in the far wake.