## 5 Analysis of Experimental and Simulation Results
### Uniform Water Body Conditions
#### 5.1.2 Case 2 Working Conditions  
In Case 2, the initial velocity of the jet is 0.2 m/s, with a water depth of 0.26 m and a temperature difference of 10 \({}^{\circ}\)C compared to the ambient water. The changes in temperature field distribution of the jet discharged in a uniform water environment at intervals of 5 s, 10 s, 15 s, 20 s, 25 s, and 30 s are illustrated in Figure 7 under the experiment conditions. Figure 5: Simulation calculated results of the thermal jet temperature field. Figure 6: Vertical variation of spindle linear velocity of thermal jet. Upon doubling the initial velocity of the jet, it is observed that when the jet discharge time reaches 5 s, there is no longer an upward trend in the jet movement. Additionally, the jet temperature rapidly decays, resulting in a temperature difference of approximately 4 \({}^{\circ}\)C with the ambient water body. This represents a temperature decay of 55%, and it is noted that the temperature diffusion area is predominantly dominated by horizontal direction. By 10 s, a further decline in the jet temperature is observed, with the resultant temperature difference from the ambient water body being about 2 \({}^{\circ}\)C. Moreover, it is found that at this point, the vertical height of the jet remained within 5 cm. Subsequently, at around 15 s, there is evidence of buoyancy, as indicated by an increase in floating height to within an interval between 5 and 10 cm. As we approach 20 s, due to its high initial velocity, it can be seen that there has been minimal change in uplift height while maintaining motion dominantly along a horizontal trajectory towards rightward diffusion. Finally, at around 30 s, significant diffusion of the jet's heat field, reaching up to approximately 50 cm, is recorded. It should also be noted that the uplift height experienced minimal change during this period, and remains within an interval between 10 and 20 cm. From the trends in the diffusion region of the thermal jet temperature field, it can be observed that when the jet velocity is doubled, there is a significant decrease in the upward trend of the jet temperature. This results in a shift towards horizontal direction dominance in temperature diffusion. As a consequence, there is a reduction of 34.6% in the far-end jet temperature's upward height, while the horizontal outgoing diffusion distance increases by 20%. Furthermore, it is noted that the jet temperature does not diffuse to the water surface. The area of the temperature dissipation region shows a significant increase, and there is an acceleration in the speed of temperature dissipation. By the 30 s mark, it is found that up to 50% of the thermal jet's temperature dissipation area can be achieved. The analysis is based on selected moments (5 s, 10 s, 15 s, 20 s, 25 s, and 30 s) under Case 2 simulation calculations as shown in Figure 8.  
Based on the diffusion trend of the jet temperature field, it is observed that the simulation results are in agreement with the experimental data. Specifically, during the first 15 s of jet discharge, there is no significant increase in the jet temperature. The vertical temperature diffusion remains relatively unchanged until this point. Subsequently, an upward trend in the jet temperature is observed, which can be attributed to a temperature difference of over 5 \({}^{\circ}\)C between the jet and ambient water, accounting for 80% of the increase. Additionally,  
Figure 7: Temporal variation of the thermal jet temperature field under the experimental conditions. it is noted that an increase in jet velocity inhibited the rate of temperature decay and prolonged the time taken for temperature dissipation. As the duration of jet discharge increased from 15 s to 30 s, there is a gradual expansion in the area experiencing temperature diffusion, with a difference of 2-4 \({}^{\circ}\)C compared to the ambient water body temperatures. This expansion corresponds to an increase from 40% to 75%.