First stages of aeronautical high-pressure turbines are subjected to significant inlet distortions generated by the combustor system. These disturbances are characterized by velocity and temperature fluctuations convected downstream by the flow. Such perturbations are commonly defined as vorticity and entropy waves and interact with the turbine stages affecting the aerodynamic performance, the heat exchange and generating indirect noise. Moreover, the presence of a swirling flow highly influences the convection and migration of the entropy wave, thus its interaction with the stage. The paper presents an in-depth study of the impact of the swirling flows on the entropy wave evolution by means of experimental campaigns and numerical simulations. Experimental campaigns have been carried out at Politecnico di Milano where a high-pressure turbine rig was equipped with a novel combustor simulator able to generate entropy waves and swirl profiles. Numerical simulations have been performed at the University of Florence by applying time accurate simulation schemes, including incoming disturbances, implemented in the CFD TRAF code. Two different entropy waves (featuring frequencies of 10 and 110 Hz) injected in a counterclockwise swirling region at midspan have been analyzed at two clocking positions: passage aligned and vane aligned. An excellent agreement is found between experimental acquisitions and numerical results: both show an important reduction of the temperature fluctuations through the stage and highlight the effect of the swirling profile on secondary flows and blade wakes. The extensive comparison reported in the paper validates the numerical approach (based on URANS simulations post-processed by a dedicated filtering technique) which has been further applied to study the impact of swirling flows with an opposite rotation (clockwise). The broad numerical investigation combined with the extensive experimental campaign leads to a deeper understanding of the aerodynamic, thermal, and acoustic implications related to entropy wave evolution in a swirling flow highlighting the interaction phenomena and suggesting how to minimize the impact of entropy waves by comparing the results of the different injection positions and swirling flow directions.