## 3 Results
### Physics of the Side-Jets Formation Phenomenon
#### 3.3.3 Impact of \(Ti\) on the Formation of Side-Jets  
The mechanism of side-jet formation has been explained in the previous section. Now it is analysed whether the above explanations are valid for the cases with larger \(Ti\). In an analogy with Figures 11 and 12, the results obtained for the cases with \(Ti=0.1\%\) and \(Ti=1.0\%\) are presented in Figures 13-16. As can be seen, for \(Ti=1.0\%\), the side-jets do not appear either in the Cartesian coordinate or cylindrical systems. They occur for \(Ti=0.1\%\), but their number and azimuthal locations differ. In the Cartesian system, contrary to what we can see in the case with \(Ti=0.01\%\), the occurrence of side-jets is random and not along the diagonal directions. Worth noticing is the fact that they expand in the radial direction over a larger distance and are more irregular than in the case with \(Ti=0.01\%\). The random occurrence of the side-jets is caused by the disturbance generated at \(Ti=0.1\%\) that overwhelms the disturbances related to the azimuthal mesh non-uniformity. A larger irregularity of the side-jets also takes place in the cylindrical coordinate system. As can be seen in Figure 15, three or four side-jets appear at particular time instances, but they are not as well formed as for the case with \(Ti=0.01\%\) (Cf. Figure 12). Summing up the above observations, one can say that: (i) a high level of natural turbulent intensity prevents the formation of the side-jets, as already mentioned in the introduction; (ii) the mechanism that triggers the development of the rib vortices creating the side-jets has twofold nature, i.e., strictly numerical, stemming from the azimuthal non-uniformity of the mesh in the Cartesian coordinate system, and physical, originating from the non-uniformity and randomness of the disturbances at the nozzle exit in the cylindrical coordinates; (iii) in the Cartesian coordinate system, the localisation and number of the side-jets is random only when the naturally generated dist  
Figure 12: Contours of an instantaneous axial velocity \(U_{x}/U_{0}\) at the plane perpendicular to the jet axis \(x/D=9\) for the case \(E-Cyl-Ti_{0.01}\). Figure 13: Contours of an instantaneous axial velocity \(U_{x}/U_{0}\) at the plane perpendicular to the jet axis \(x/D=9\) for the case \(E-Car-Ti_{0.1}\). the turbulence intensity, \(Ti=1.0\%\), \(Ti=0.1\%\) and \(Ti=0.01\%\). For natural jets, the comparison of the solutions was performed based on instantaneous and time-averaged results. For the cases with \(Ti=1.0\%\) and \(Ti=0.1\%\), the solutions were almost independent of the coordinate system. On the other hand, significant differences were observed for \(Ti=0.01\%\). In this case, both the potential core length and localisations of the maxima of the fluctuations diverged substantially. Analysis of the excited jets concentrated on the identification of the side-jets and the explanation of the mechanism of their formation. These computations were also performed in the Cartesian and cylindrical coordinate systems. In the former case, for \(Ti=0.01\%\), the obtained results revealed the formation of four side-jets extending only along the diagonals of the computational domain. Such an unnatural behaviour was attributed to the non-uniform mesh resolution along the azimuthal direction, leading to different levels of derivative approximation errors. This phenomenon was diminished for the case with \(Ti=0.1\%\), for which the natural disturbances introduced at the nozzle exit dominated over the numerically induced disturbances. In this case, the side-jets had the tendency to appear in a definitively more random manner. For \(Ti=1.0\%\), the side-jets did not appear. The application of the cylindrical coordinate system excluded the azimuthal non-uniformity of nodes, and in this case a random number and location of the side-jets were observed. The conducted analysis showed that the mechanism leading to the formation of the side-jets is essentially the same in both coordinate systems, i.e., it is a localised disturbance.