## 5 Results and Discussion
### Wave Patterns  
Figure 12 depicts wave patterns around the ship model at an even keel and different trims. When a ship enters shallow water, several changes occur due to the interaction between the ship and the bottom. Namely, the fluid accelerates, and the pressure under the hull decreases, which may result in significant changes in sinkage and trim. This leads to an increase in frictional and wave resistance along with the changes in the wave pattern generated around the hull. The effects of side boundaries, i.e., banks are similar to those experienced in shallow water. The Froude number relevant for the ships in restricted waterways is the one calculated based on the water depth (\(Fn_{h}\)). Speeds corresponding to the \(Fn_{h}<1\) are denoted as subcritical speeds, while the ones corresponding to \(Fn_{h}>1\) as supercritical speeds [28]. Around the critical speed solitary waves may be generated that move ahead of the ship. At speeds well below \(Fn_{h}=1\), the wave system consists of a transverse wave system and a divergent wave system propagating away from the ship. Within this study, the Froude number based on the water depth is \(Fn_{h}=0.469\), and the wave system of transverse and divergent waves along with the Kelvin wave pattern can be observed similarly to the one in unrestricted water. As the speed approaches the critical one  
Figure 11: Contribution of resistance components for the SSTKO turbulence model.  
Figure 10: Contribution of resistance components for the RKE turbulence model.  
a significant amplification of wave resistance occurs, while at speeds greater than critical, the resistance again decreases. In confined water, the wave system around the ship hull consisting of transverse and divergent waves interferes with the waves reflected against the side walls of the channel, which can be noticed in Figure 12. Under such conditions complex wave patterns are generated considering that waves propagate from different directions, which is consistent with findings available in the literature [12; 29]. In the case of a trim by stern, an increase in wave elevations behind the stern can be noticed.  
The wave elevations along the model hull at an even keel and various trims are given in Figure 13. It can be noticed that the wave elevations in the bow region are the highest for trims by stern, while in the stern region, the highest wave elevations are obtained for trims by bow. In comparison to an even keel wave systems obtained for all analyzed trims are shifted towards the stern. Changes in the wave elevations for trims by stern in comparison to an even keel are more significant in the bow region than in the stern region. Higher wave elevations are linked to an increase in the pressure resistance (Table 9). The lowest wave elevations are obtained for the largest analyzed trim by bow, which corresponds to  
Figure 12: Wave patterns around the hull at an even keel and various trims.  
the larger decrease in the pressure resistance of \(-11\%\). By comparing the wave elevations at the centerline in front of the hull it can be noticed that the lowest wave elevations are obtained for the trim of \(0.4^{\circ}\), while the highest ones correspond to trims by stern (Figure 14). The underwater shape of the bulbous bow is very important, especially for the wave-making resistance. As it changes with the change in trim it affects the formation of the bow wave system.