The use of dual heat injection to infer scalar covariance decay in grid turbulence

Abstract

Thermal fluctuations introduced into decaying grid turbulence at two different downstream locations are shown to be initially correlated and this correlation decays with distance from the grid. The fluctuations are introduced by placing two mandolines (Warhaft & Lumley 1978) at different distances downstream from the grid. The sum of the thermal variances produced by each mandoline operating separately, $\overline{\theta^2_1}+\overline{\theta^2_2}$, is significantly less than the total variance produced by both mandolines operating simultaneously, $\overline{(\theta_1+\theta_2)^2} = \overline{\theta^2_1} + \overline{\theta^2_2} + \overline{2\theta_1\theta_2} $, i.e. the deficit is due to the covariance term $\overline{2\overline{\theta_1\theta_2}}$. This covariance is responsible for a cross-correlation, $\rho = \overline{\theta_1\theta_2}/(\overline{\theta_1^2}\overline{\theta^2_2})^{\frac{1}{2}}$, as great as 0·6. The decay of $\overline{\theta_1\theta_2} $ and ρ is studied for various initial input thermal scale sizes and for various input locations. It is shown that the covariance follows a power-law decay, the exponent varying from - 5·5 if the thermal fluctuations are introduced close to the grid where the turbulence dissipation rate is large and the flow is inhomogeneous to - 4 if they are introduced further downstream (x/M ≥ 10, where x is the distance from the grid and M is the grid mesh length) in the region where the approximately isotropic turbulence is beginning to develop. The decay rate of $\overline{\theta_1\theta_2} $ and ρ was insensitive to the intensity of the thermal fluctuations. In all these experiments the cross-correlation between velocity and temperature fluctuations was very small (∼ − 0·05) and temperature was a passive additive. The results, which appear to be the first quantitative measurements of the rate of destruction of scalar covariance and hence of the mixing rate between two scalars, are shown to provide good confirmation of recent predictions of the decay of ρ by the second-order closure techniques of Lumley (1978 a, b).