This paper presents the capability of a numerical code, isis-cfd, based on the solution of the Navier–Stokes equations, for the investigation on the hydrodynamic characteristics of a marine propeller in open water. Two propellers are investigated: the Istituto Nazionale per Studi ed Esperienze di Architectura Navale (INSEAN) E779A model in straight-ahead flow and the Potsdam Propeller Test Case (PPTC) model in oblique flow. The objectives of this study are to establish capabilities of various turbulent closures to predict the wake propeller and to predict the instability processes in the wake if it exists. Two Reynolds-averaged Navier–Stokes (RANS) models are used: the k–ω shear stress transport (SST) of Menter and an anisotropic two-equation explicit algebraic Reynolds stress model (EARSM). A hybrid RANS–large eddy simulation (LES) model is also used. Computational results for global flow quantities are discussed and compared with experimental data. These quantities are in good agreement with the measured data. The hybrid RANS–LES model allows to capture the evolution of the tip vortices. For the INSEAN E779A model, the instability of the wake is only predicted with a hybrid RANS–LES model, and the position of these instabilities is in good agreement with the experimental visualizations.