## 1 Introduction  
Investigations devoted to circular jets have both a fundamental character and practical implications. In the former case, they concentrate on a deeper understanding of mixing processes, hydrodynamic instability and interactions between vortices. In the latter, the need for jet dynamic analysis stems from the fact that jets are commonly used in various technical devices, e.g., as fuel injectors in combustion chambers, as burners or as the ends of paint sprayers. A very interesting and still not fully understood phenomenon accompanying jet flows is the formation of side-jets. They were observed experimentally in globally unstable [1; 2; 3; 4; 5] and strongly forced [6; 7] round jets as inclined streams released from the jet at a certain angle to the jet axis. The necessary conditions for the occurrence of side-jets are the existence of strong vortical structures in the near field of the jet and a low level of turbulence intensity. [PERSON] et al. [1] claimed that the primary mechanism of the formation of side-jets was the azimuthal instability of vortical structures (Widnall instability [8]), which causes the deformation of vortices and ejects fluid away from the jet stream. The subsequent experimental [6] and numerical [9] analyses showed that the generation of the side-jets was not directly caused by the Widnall instability of vortex rings but rather by the occurrence of pairs of streamwise vortices originating from the instability of the braid region. However, the mechanism leading to this phenomenon has not been fully understood so far and needs further studies. Contemporary computational fluid dynamics (CFD), which offers a wide range of numerical methods, allows for very accurate predictions of complex phenomena occurring in fluid flows and seems to be a very useful tool to explain and understand the phenomenon of the side-jets. As shown by [PERSON] et al. [10], where the global instability in a round jet using a large eddy simulation (LES) was investigated, the formation of the side-jets turned out to be very sensitive to small disturbances such as inlet turbulence intensity, mesh non-uniformity or errors stemming from discretisation. The LES performed on the Cartesian mesh showed the occurrence of four equally spaced side-jets aligned with the mesh lines, while in the experiment [1], the number of the side-jets was between 2 and 6 and their orientation was rather random. The authors claimed that the mechanism of the side-jet formation was reflected accurately, and the only difference between experimental and numerical investigations was the mechanism introducing the perturbation, namely one that was random (a real situation) and one that was determined by the Cartesian mesh. The formation of four side-jets equally spaced in the azimuthal direction could also be observed in the direct numerical simulation (DNS) of forced jets [11], where the effect of varicose perturbation was examined. The authors did not pay attention to the side-jet phenomenon, but the results of vorticity and streamwise velocity presented showed the formation of four side-jets, which were oriented along the mesh lines or diagonals of the computational box. [PERSON] and [PERSON] [12] analysed the formation of the side-jets in excited round jets using the LES method in the Cartesian and cylindrical coordinate systems. The obtained solutions suggested that the occurrence and number of side-jets in some regimes are influenced by the mesh topology. A strong impact of the Cartesian mesh on the orientation and localisation of the side-jets was also noted in a DNS study of high-p jets [13]. The results showed the emergence of four side-jets; however, the majority of attention was paid to the effect of the occurrence of the side-jets rather than the mechanism of their formation. The present work is focused on the accuracy of LES of the turbulent jets subjected to various turbulence intensity levels. The solutions obtained for natural and excited jets in the Cartesian and cylindrical coordinate systems are compared.