## 3 Results and Discussion
### The Mean Velocity of the Double-Walled Confined Waterjet  
Profiles of the mean velocity at selected downstream locations \(x/D=20\) on the vertical (\(X\)-\(Y\)) and horizontal (\(X\)-\(Z\)) planes for four double-walled confined cases are presented in this section. As is shown in Figure 7, the centerline velocity is greater than at other positions. With the location moving to both sides, the velocity decreases rapidly in all cases. Taking the features as a whole, the distribution of axial mean velocity of the \(X\)-\(Y\) plane is symmetrical about its own centerline. However, in each case, the plot shows various features according to different widths. The diffusion boundary of the submerged waterjet becomes narrower as the confined width increases. To be more specific, taking \(U/U_{c}=0.6\), for example, the dimensionless boundary lengths are 5, 4, 3.5, 2 when \(H/D=5\), 10, 13, 15 respectively. The double-walled confined condition is able to make the jet flow spread to both sides. Another distinction shown from Figure 7 is that the maximum mean velocity of the centerline increases as the confined width H/D increases. When the confined width \(H/D=5\), the maximum velocity \(U/U_{c}\) is about 0.9 and when it is 15, the value is about 1.2. It is believed that this kind of phenomenon can be explained by the following reasons. On the one hand, the submerged waterjet flow is close to wall at the stream location. The wall is not completely smooth so as to hold back and disturb the flow field. With the confined width decreasing, the force of friction and disturbance become larger and energy dissipation increases. On the other hand, because of the existence of the double-wall, the development of the waterjet flow at the vertical direction is limited, which results in the flow spreading along the horizontal direction. The axial velocity component decreases and the radial velocity component increases. Figure 8 shows the mean velocity in the axial direction at the vertical plane \(X\)-\(Z\). It can be seen that the axial mean velocity distribution of the vertical plane has similarities to the axial mean velocity distribution of the horizontal plane. In other words, from the central axis to both sides, the speed is decreased and it is symmetrically distributed with respect to the axis. However, the latter speed  
Figure 7: Axial mean velocity of the horizontal plane (\(X\)-\(Y\)). distribution is more irregular. When \(H/D=5\), the jet mean velocity distribution is uniform and has a trend of pulsating. When \(H/D=15\), the jet mean velocity shows a ridge distribution which is similar to that of the free jet. That is to say, the double-walled confined waterjet velocity distribution of the axial direction in the vertical plane is affected significantly by the confined width. As the confined width becomes smaller, the velocity distribution becomes more gentle. The presence of a limited condition forces the jet to develop horizontally. With the decrease of confined width, the impacting position of the wall on the jet will advance. That means that the confined width has a spatial advance effect on the transition process. We can also observe some other rules from Figure 8. The velocity distributions under different operating conditions are not completely symmetrical to the axial centerline. For instance, when \(H/D=10\), the symmetry axis of axial velocity is \(Z/H=0.8\), and when \(H/D=15\), the symmetry axis is \(Z/H=-0.1\). We believe that this is due to the following reasons. Firstly, the time of image acquisition is in the development period of the vortex, and the instantaneous flow velocity distribution is asymmetric. Secondly, the number of images acquired is too small to average the speed for a long enough time. Figure 9 shows the mean velocity in the radial direction in the vertical plane \(X\)-\(Z\). Although the speed distribution in Figure 8 is more chaotic, there are rules to follow.