Turbulent dispersion of passive scalar released from line sources in a fully-developed smooth plane-channel and a rib-roughened open-channel are studied using direct numerical simulations (DNS). In order to investigate the effects of wall anisotropy on the plume development, the line sources are aligned either in the spanwise direction parallel to the wall or in the vertical direction perpendicular to the wall. The investigation into the turbulent transport processes of the momentum and concentration is conducted in both physical and spectral spaces, based on a systematic analysis of the statistical moments of the velocity and concentration fields, probability density functions (PDFs) of the scalar field, and the characteristic wavelengths of energetic eddies that dominate turbulent mixing processes. In the single vertical line source case, it was observed that the meandering ratio is small near the ground and within the turbulent diffusive stage, and PDFs of concentration fluctuations are sensitive to both the wall-normal distance and the downstream distance from the source. In the case of plume dispersion over a rib-roughened surface, it is observed that as the mean plume development enters the long-range dispersion stage, the decay rate of the mean concentration field begins to feature a constant slope of -3/2, while the vertical spread of the mean plume exhibits a constant slope of 1/3. In the case of dual plume mixing, it is observed that a smaller source separation tends to facilitate a more rapid growth in the correlation coefficient of two instantaneous plumes. In the near-source regions, the maximum coherency spectrum is produced at lower frequencies indicating that dual-plume mixing is dominated by the external flapping effects of large-scale eddy motions. However, in the far downstream region of the sources, the coherency spectrum at higher frequencies increases significantly, indicating that the spread of the total plume is larger than all scales of turbulent eddies, such that they all contribute to the in-plume mixing of the dual plumes.