This paper presents detailed Euler–Euler Scale-Adaptive Simulations of the dispersed bubbly flow in a square cross-sectioned bubble column. The main objective is to investigate the potential of this approach for the prediction of bubbly flows with anisotropic liquid velocity fluctuations. The set of physical models describing the momentum exchange between the phases was chosen according to previous experiences of the authors. Experimental data and Euler–Euler Large Eddy Simulation are used for comparison. It was found that the presented combination of sub-models provides good agreement with experimental data for the mean flow and liquid velocity fluctuations. The energy spectra of the resolved velocity obtained from the simulations are presented and compared to the experimental spectra.