Experiments and simulations of passive scalars released from concentrated sources in turbulent channel flow

Turbulent mixing of a passive scalar ($\theta$) is studied by means of experiments and numerical simulations in turbulent channel flow, with an emphasis on the scalar dissipation rate ($\varepsilon_{\theta}$). The scalar (temperature) is injected at small scales by a heated line source, aligned in the spanwise direction. The present experiments focus on the evolution of $\varepsilon_{\theta}$ downstream of the line source, for different wall-normal source locations. In particular, knowledge of the different components of $\varepsilon_{\theta}$ (i.e., $\alpha \langle (\partial \theta / \partial x)^2 \rangle$, $\alpha \langle (\partial \theta / \partial y)^2 \rangle$, and $\alpha \langle (\partial \theta / \partial z)^2 \rangle$, where $\alpha$ is the thermal diffusivity) enable the quantification of the small-scale passive scalar statistics, and their (presumed) return to isotropy from an initially anisotropic injection. Measurements of temperature derivatives were performed by means of cold-wire thermometry. A direct numerical simulation was also undertaken to provide complementary data, difficult to obtain experimentally. The velocity field was independently computed using the freely-available channel flow code of Dr. John Gibson (http://www.channelflow.org). The advection-diffusion equation was solved using a third-order scheme with the flux integral method (Leonard \emph{et al.}, Appl. Math. Modelling, 1995).