## 3 Results
### Physics of the Side-Jets Formation Phenomenon
#### 3.3.2 Mechanism of the Formation of Side-Jets  
The subsection focuses on the role of the rib vortices in the formation of the side-jets. In Figure 8a,b, it can be seen that they are pushed outside by the vortex ring. The contours of the streamwise vorticity and radial velocity are shown in the cross-sections passing through one pair of the ribs. Note that the streamwise vortices are counter-rotating, which is additionally visualised by the velocity vectors. This causes the ejection of the fluid from the jet core towards the jet periphery, as can be inferred based on large values of the radial velocity. This stream forms a side-jet. Note that the presented scenario is exactly the same in the Cartesian and cylindrical coordinate systems, and the only difference is the mechanism of the generation of rib vortices. The influence of the turbulence intensity level on these phenomena will be presented in the next subsection. The formed side-jets are presented in Figures 9 and 10. They show the iso-surfaces of the axial velocity (\(U_{x}/U_{0}=0.2\)) and the axial velocity distribution in the cross-sections perpendicular to the jet at the axial distance \(x/D=9\). As can be seen in Figure 9, showing the solution obtained in the Cartesian coordinate system, there are four side-jets located at the diagonals of the computational domain that correspond to the directions of the worst mesh resolution along the radius, as discussed above. The solution obtained in the cylindrical coordinate system, presented in Figure 10, is significantly different. In this case, only three side-jets are observed, and they are randomly distributed along the azimuthal direction. During the simulation, the number of side-jets and their localisation in the cylindrical coordinates change and, as suggested above, seem to have unpredictable nature. Figure 11 shows the contours of an instantaneous axial velocity in the cross-section located at \(x/D=9\), where the side-jets are clearly visible. Particular subfigures refer to the solutions at selected time moments spaced by \(\Delta T=10D/U_{0}\). It can be seen that in the Cartesian system, the side-jets are always in the same four places, and only the values of the velocity inside them changes, as this depends on the strength of the counter-rotating vortices in the ribs. This, on the other hand, is connected to the time-varying strength of the toroidal vortices that push them away from the jet core. In the case of the cylindrical system, the situation is different; see Figure 12. Here, the side-jets are formed in different locations; the velocities inside them differ, and moreover, there are time moments, e.g., Figure 12c, when the side-jets disappear.  
Figure 11: Contours of an instantaneous axial velocity \(U_{x}/U_{0}\) at the plane perpendicular to the jet axis axis \(x/D=9\) for the case \(E-Car-Ti_{0,01}\).  
Figure 10: Iso-surfaces of the axial velocity \(U_{x}/U_{0}=0.2\) (**a**) and contours of axial velocity \(U_{x}/U_{0}\) at the plane perpendicular to the jet axis (**b**). The results are obtained for the case \(E-Cyl-Ti_{0,01}\).  
Figure 9: Iso-surfaces of the axial velocity \(U_{x}/U_{0}=0.2\) (**a**) and contours of axial velocity \(U_{x}/U_{0}\) at the plane perpendicular to the jet axis (**b**). The results are obtained for the case \(E-Car-Ti_{0,01}\).