Turbulent flows of liquid nitrogen jets at near-critical and supercritical pressures are investigated by turbulence models (RANS) and a large eddy simulation (LES). To consider real-fluid effects, two real-fluid equations of state (EOS) are implemented into the numerical procedure and the normalized static enthalpy is introduced to describe the turbulent mixing under supercritical conditions. The pressure-velocity-density coupling is obtained by the modified PISO algorithm. The relative performance of six convection schemes and the predictions of four turbulence models for the different EOSs are compared with the available data. From the results, the suitable adoption of real-fluid EOS is more significant than the selection of turbulence model for the numerical performance. Additionally, the effects of SGS models are examined for the LES predictions using the different EOSs. The importance of real-fluid EOS is similarly found in the LES results. The coherent structures are strongly dependent on the different EOSs than SGS models. The results display that the selected RANS models need to be extended for supercritical fluid flows. Finally, the effects of turbulence models and SGS models on the jet spreading rate are discussed. (C) 2012 Elsevier B.V. All rights reserved.