We report on the examination of several approaches to simulate computationally the unstable regime of a model Kaplan turbine operating at off-design load. Numerical simulations complemented by laboratory experiments have been performed for a 60:1 scaled-down laboratory turbine model using two Reynolds-averaged Navier–Stokes (RANS) models (linear eddy viscosity model (LEVM), and a Reynolds stress model (RSM), including realizable k-ε, k-ω SST, and LRR), detached eddy simulation model (DES), and large eddy simulation model (LES). Unlike the LEVM, the RSM, DES, and LES reproduced the mean velocity components and the intensities of their fluctuations and pressure pulsations well. The underperformance of the LEVM is attributed to the high eddy viscosity as a consequence of an excessive production of the turbulent kinetic energy due to the models’ inability to account for the turbulent stress anisotropy and the stress-stain phase lag, both naturally accounted for by the RSM. This led to a much larger modelled and a smaller resolved turbulent kinetic energy compared to those in the RSM.