## 3 Results and Analysis
### Analysis of Flow Field and Flow Characteristics  
Injecting freshwater into the cavity, which is akin to a submerged wall jet, as illustrated in Figure 14, creates complex and variable flow fields due to water injection, fluid convection, and boundary expansion. Initially, the cavern is categorized into the main flow, circulation, and reflux regions based on the flow characteristics, delineated by the null streamwise velocity line (v = 0) and the inflection point (\(\partial\mathrm{2v}/\partial\mathrm{y}\mathrm{2}=0\)) of the velocity profile [32; 40]. The main flow region exhibits a higher velocity due to momentum from the injected freshwater, which quickly diminishes post-injection. Meanwhile, brine flow forms a vortex due to forced convection; this initial flat vortex expands as the cavity grows upwards, though its intensity decreases, and its center shifts towards the outlet. Figure 15 displays the flow velocity, streamline distribution, and vortex shape during the second leaching stage. Forced convection at the injection point creates a single vortex from the first stage. As the flow momentum diminishes, another vortex begins to form in the dissolution section, eventually merging into a larger single vortex as the cavity expands.  
During the later leaching stages, despite cavern expansion, the dimensions of flow and reflux regions stabilize, with a constant flow rate of 200 m\({}^{3}\)/h. The flow strength diminishes as the cavern enlarges, resulting in more vortices and a weaker flow intensity. From the third to the fifth stages, vortices consistently form in the dissolution section, merging with the previous vortices as expansion continues. After each stage, the vortex center shifts to the dissolution section's adjacent cavity, away from the outlet. By the fifth stage, with the outlet over 200 m from the injection point, gravitational differentiation surpasses the forced convection's impact on the brine, causing the denser brine to sink and the lighter brine to rise, forming a new weaker vortex.  
Figure 12: Diagram of the thermal convection direction and the concentration contour of brine in the cavity. (The blue arrows represent thermal convection, and the curves represent the concentration contour line).  
Figure 13: The cavern shape under different temperatures after 10 days of leaching.  
The vortex cyclically circulates fluid within the cavity, enhancing the brine convective diffusion speed. This process replaces high-concentration brine near the cavity wall with lower concentration brine, leading to faster leaching rates and higher construction efficiency. Cavity expansion is primarily driven by dissolution and erosion under forced convection. Initially, erosion dominates in the dissolution cavern section, but dissolution becomes the primary factor over time. The expansion rate of the formed cavity section depends on the vortex strength, as erosion gives way to dissolution. As shown in Figure 16, the dissolution section expands the quickest, with expansion slowing in the sections closer to the outlet due to a diminished vortex intensity.  
Figure 14: Contours of velocity magnitude at vertical section (X = 0 m) during first stage. (The red arrow line represents the streamline of brine).  
Figure 15: Contours of velocity magnitude at vertical section (X = 0 m) during second stage (The red arrow line represents the streamline of the brine).