The structure and development of the scalar wake produced by a single line source are studied in decaying isotropic turbulence. The incompressible Navier–Stokes and the passive-scalar transport equations are solved via direct numerical simulations (DNS). The velocity and the scalar fields are generated by simulating Warhaft's (1984) experiment. The results for mean and r.m.s. scalar statistics are in good agreement with those obtained from the experiment. The structure of the scalar wake is examined first. At initial times, most of the contribution to the scalar variance is due to the flapping of the wake around the centreline. Near the end of the turbulent convective regime, the wake develops internal structure and the contribution of the flapping component to the scalar variance becomes negligible. The influence of the source size on the development of the scalar wake has been examined for source sizes ranging from the Kolmogorov microscale to the integral scale. After an initial development time, the half-widths of mean and scalar r.m.s. wakes grow at rates independent of the source size. The mixing in the scalar wake is studied by analysing the evolution of the terms in the transport equations for mean, scalar flux, variance, and scalar dissipation. The DNS results are used to test two types of closures for the mean and the scalar variance equations. For the time range simulated, the gradient diffusion model for the scalar flux and the commonly used scalar dissipation model are not supported by the DNS data. On the other hand, the model based on the unconditional probability density function (PDF) method predicts the scalar flux reasonably well near the end of the turbulent convective regime for the highest Reynolds number examined. The scalar source size does not significantly influence the models' predictions, although it appears that the time-scale ratio of mechanical dissipation to scalar dissipation approaches an asymptotic value earlier for larger source sizes.