Asymptotic behaviour of a scalar in an axisymmetric final period turbulent wake

Abstract

The behaviour of a conserved scalar field in the final period of an axisymmetric turbulent wake is investigated theoretically. Explicit formulae are derived for the behaviour, during and just prior to the scalar field final period, of quantities such as mean concentration, concentration correlations and velocity–scalar or vorticity–scalar cross-correlations. In particular, if τ is the time measured from a virtual origin it is shown that scalar intensity, which decays as τ−5/2, is more persistent asymptotically than turbulence intensity, which displays a τ−7/2decay. By deriving the scalar field structure as perturbed by the Reynolds stresses acting on mean scalar gradients in the final period it is shown, e.g., that the mean field perturbation dies out at least as rapidly as τ−4, whereas the mean field itself decays as τ−1. Numerical results are presented to display the spatial structure of typical scalar correlations and velocity–scalar cross-correlations, which are compared where possible with non-asymptotic measurements in the wake of a heated sphere.