A turbulent methane-oxygen diffusion flame is studied using a direct numerical simulation setup. The operating regime and turbulence characteristics are chosen to resemble those of a modern methane rocket combustor. Local flame characteristics and dimensionless numbers are defined and evaluated, and their relationship with the turbulent kinetic energy transport budget is studied. Positive net turbulence generation is observed in the reaction shear layer. It is found that the underlying mechanisms for these results are similar to those encountered in premixed flames, with pressure terms acting as the primary turbulent kinetic energy sources. Models for predicting turbulent transport through mean pressure gradients, fluctuating pressure gradients, and turbulent flux of turbulent kinetic energy are adapted. The accuracy of the proposed formulations is assessed, and the involved challenges are discussed.