Results are presented from highly resolved three-dimensional simulations of turbidity currents down a slope into a stratified saline ambient, for various stratification and particle settling velocity congurations. The general behaviour of turbidity currents is discussed and visualized. The unstable nature of the flow is then further examined visually through three-dimensional representations of isosurfaces of constant particle concentration. The lobe and cleft instability plays a key role in the transition from two-dimensional Kelvin-Helmholtz instabilities to a fully developed three-dimensional turbulent flow. The instability is described in terms of wavelength and sensitivity to the Reynolds numbers. The front velocity is then computed for various configurations of stratification and particle settling velocity. The results are compared directly to experimental data by Snow and Sutherland and to a new scaling law, with close agreement, confirming the ability of highly resolved numerical simulations to capture the physics of such flows. The time and space dependent entrainment velocity of the ambient fluid into the current is discussed. The intrusion of the current into the ambient fluid is then investigated and compared to the experimental results of Snow and Sutherland, an existing scaling law proposed by those authors, and a new predictive model. The numerical results help validate the scaling law of Snow and Sutherland, but also highlight its sensitivity to the choice of entrainment coefficient and its limitations in low entrainment but high settling rate scenarios. The new scaling relation for the intrusion depth is shown to be more robust and predictive in such cases. The energy budget of the flow is analyzed in order to explain the governing processes in terms of energy transfers, with a focus on energy losses and potential to kinetic energy transfers.