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Experimental and theoretical studies of fluctuations in nucleus-nucleus interactions at high energies have started to play a major role in understanding of the concept of strong interactions. The elaborated procedures have been developed to disentangle different processes happening during nucleus-nucleus collisions. The fluctuations caused by a variation of the number of nucleons which participated in a collision are frequently considered the unwanted one. The methods to reduce the impact of these fluctuations in fixed-target experiments are reviewed and tested. They can be of key importance in the following ongoing fixed-target heavy-ion experiments: NA61/SHINE at the CERN SPS, STAR-FXT at the BNL RHIC, BMN at JINR Nuclotron, HADES at the GSI SIS18 and in future experiments such as NA60+ at the CERN SPS, CBM at the FAIR SIS100, JHITS at J-PARC-HI MR.
We propose to use the hadron number fluctuations in the limited momentum regions to study the evolution of initial flows in high energy nuclear collisions. In this method by a proper preparation of a collision sample the projectile and target initial flows are marked in fluctuations in the number of colliding nucleons. We discuss three limiting cases of the evolution of flows, transparency, mixing and reflection, and present for them quantitative predictions obtained within several models. Finally, we apply the method to the NA49 results on fluctuations of the negatively charged hadron multiplicity in Pb+Pb interactions at 158A GeV and conclude that the data favor a hydrodynamical model with a significant degree of mixing of the initial flows at the early stage of collisions.