Anisotropy of the scalar field downstream of a concentrated source in turbulent channel flow

The scalar field downstream of a concentrated line source in fully-developed, high-aspect-ratio turbulent channel flow is studied\footnote{R.A. Lavertu and L. Mydlarski, 2005. {\it J. Fluid Mech.}, {\bf 528}, p. 135.}. Such a flow was selected to isolate the role of the inhomogeneity, which is confined to only one direction (i.e., the wall-normal direction). The scalar under consideration is temperature and is measured by means of cold-wire thermometry. Small-scale statistics of the scalar field, with an emphasis on the scalar dissipation rate ($\langle\varepsilon_\theta\rangle$), are studied. The anisotropy of the different components of $\langle\varepsilon_\theta\rangle$ will be presented, as well as their downstream return to isotropy. A comparison with the experiments of Rosset et al.\footnote{L. Rosset, P. Parantho$\ddot{e}$n, J.-C. Lecordier, and M. Gonzalez, 2001. {\it Phys. Fluids}, {\bf 13}, p. 3729.} indicates that the anisotropy $\langle\varepsilon_{\theta_y}\rangle / \langle\varepsilon_{\theta_x}\rangle$ downstream of a centreline source in channel flow is smaller that observed in turbulent plane jets.