## 5 Analysis of Experimental and Simulation Results
### Thermally-Stratified Water Body Conditions
#### 5.2.3 Case 7 Working Conditions  
In Case 7, the initial velocity of the jet is 0.1 m/s, the depth is 0.26 m, and the temperature difference with the ambient water is 25 \({}^{\circ}\)C, with a background stratification temperature difference of the ambient water at 4 \({}^{\circ}\)C. The initial velocity and depth of the jet remain unchanged from Case 5 conditions; however, there has been a 2.5 times increase in the initial temperature difference of the jet. Under these experimental conditions, Figure 18 illustrates changes in the temperature field distribution of the jet discharged into a uniform water environment at time intervals of 5 s, 10 s, 15 s, 20 s, 25 s, and 30 s.  
Figure 17: Simulation calculated results of the thermal jet temperature field. When the initial temperature difference of the jet increases significantly, there is a clear increase in the rate of the jet temperature diffusion. At 5 s, the horizontal diffusion distance of the jet temperature reaches approximately 10 cm, with minimal vertical floating. However, the vertical temperature diffusion spacing reaches 4 cm, doubling that compared to Case 5 conditions. The temperature difference between the core area of the jet and the ambient water body is about 15 \({}^{\circ}\)C. By 10 s, there is a wide range of upward diffusion for the jet temperature, with a floating rate reaching up to 0.015 m/s. The ambient temperature difference between the water body and the jet is about 8 \({}^{\circ}\)C and, at this moment, approximately 40% of the area is covered by the jet temperature diffusion. The dominant movement in vertical floating during this moment leads to only a small increase in horizontal direction for the diffusion distance. At 15 s, both the horizontal diffusion distance and the vertical floating height reach significant levels: 20 cm and 17 cm, respectively. This differs from the previous one, as in this case the jet temperature ceases to fluctuate after diffusing it to the layered interface. At this point, a portion of the temperature diffusion area appears to move horizontally towards the right side, while the main jet temperature diffusion area continues to rise. This phenomenon is attributed to the large initial temperature difference of the jet and a lower water density difference of 4.1 kg/m\({}^{3}\). The main area continues to float upwards even after diffusing to the layered interface due to a large initial temperature. When the jet temperature diffuses to the layered interface, it attenuates to around 6-8 \({}^{\circ}\)C, and since the jet density is still less than the upper water density, the jet temperature continues to diffuse upwards and floats. Between 15 s and 20 s, the diffusion rate of the jet temperature floating upwards slows down, indicating that the layered interface plays a role in inhibiting the upward diffusion of the jet temperature. During this time period, the horizontal diffusion distance of the jet temperature is only about 2 cm. At 25 s, with further attenuation of the jet temperature, its upward floating diffusion stops, and it begins moving horizontally towards the right side at a rate of 0.02 m/s, with a diffusion distance reaching 30 cm. Until 30 s, there is continued horizontal diffusion of approximately 8 cm  
Figure 18: Temporal variation of the thermal jet temperature field under the experimental conditions. towards the right side within this range where there is also an observable phenomenon of dissipation in temperatures within certain limits. The overall difference between the jet temperature diffusion area and ambient water temperature within this range is maintained at 1-4 \({}^{\circ}\)C.  
Based on measurement times under the experimental conditions (5 s, 10 s, 15 s, 20 s, 25 s, and 30 s), Case 7 simulation calculations are selected and analyzed as shown in Figure 19.  
When the initial temperature difference of the jet significantly increases, the diffusion of the jet temperature in the vertical direction rapidly floats upwards.