## 3 Key Technology in Multiphase Vortex-Induced Vibration Detection
### Formation and Evolution Mechanism of Free Sink Vortex
As shown in Figure 5a, the oil and water distribution follows a precise pattern from the start of the vortex at the free surface through a continual downward extension, eventually attaining stability. [PERSON] et al. [60] investigated the water draining from a tank to establish why an air-core vortex forms, obtaining the tangential vorticity contours for surface vortices at different intervals, as shown in Figure 5b, and discovered that angular momentum is essential to the formation of an air-core vortex. [PERSON] et al. [56] used the Helmholtz equation to calculate the ideal critical conditions for vortex generation, as illustrated in Figure 5c. The axial disturbance velocity was discovered to have a significant impact on vortex formation, and its variation pattern is similar to that of z, with a monotonically growing connection. The magnitude of the axial disturbance velocity reaches its maximum when the vortex penetrates the pipe. The development of the Rankine vortex was studied by [PERSON] et al. [61] using the enhanced interphase slip moment technique. Under the droplet slip effect, it was discovered that as droplet particles are introduced into the Rankine vortex, the Rankine vortex structure undergoes a sequence of alterations. The critical condition of vortex suction occurs during the sink vortex generation process, resulting in concentrated energy release in the flow field. The formation and dissipation of a turbulent vortex cloud, which is fundamentally connected to fluid-induced vibration, exhibits nonlinear characteristics. [PERSON] and [PERSON] demonstrated that the multiphase fluid medium was not synchronized while entering the drainage hole due to various physical features [62]. The main issue with the procedure mentioned above is that the motion laws become nonlinear due to the viscous friction of the multiphase interface and the trans-scale asynchronous transport of the Ekman layer. According to the above study, there is no mature theoretical model for the correct quantitative analysis of the vortex formation process and motion law. Still, the restricted local features may be derived only under specific ideal assumptions or combined with experimental research. In computational fluid engineering, flow features with accurate modeling of multiphase sink vortices appear to be a difficult task. Research on the vortex generation process focuses on ideal critical conditions, velocity distribution, the laminar flow state, and other factors. However, the formation mechanisms of multiphase flow under vortex turbulence and the associated dynamic features such as heat/mass transfer remain unknown and require additional research. The [PERSON] boundary layer flow theory has been widely used in oceanography [63], meteorology [64], engineering fluid calculation [65; 66], and other domains as a key tool in fluid boundary layer study. The Coriolis force, pressure gradient force, and friction in the fluid boundary layer are all taken into account by [PERSON]'s dynamic equilibrium boundary layer model. With a tiny vortex model, [PERSON] et al. [67] investigated viscous dissipative vortices. They found that low-energy vortices increased the mixing degree on the big vortex and boosted vortex mass transfer at various scales. Based on the Ekman layer hypothesis, [PERSON] et al. used a fluorescent fluid experiment to examine the Ekman layer upward flow zone at the bottom of a container. In Figure 6a,b, the dynamic evolution features of the Ekman layer were observed [68]. In the dual-pulse PIV system, [PERSON] et al. [69] discovered that the fluid field is controlled by a reverse vortex driven by elastic forces, and inertial-driven local vortices are positioned at the corner between the bottom and the column wall. [PERSON] et al. [70] discovered that vortex diffusion improves the mass transfer rate between the flow zone and vortices as the flow Reynolds number rises. In Figure 6c,d, [PERSON] et al.