## 1 Introduction  
A jet is defined as a flow state in which fluid with initial momentum flows into an ambient fluid through a vent or nozzle and mixes strongly with the ambient fluid. Jets are characterized by the flow of a fluid with initial momentum through a vent or nozzle into the ambient fluid, where it then strongly mixes [1]. The size of the initial momentum of the fluid determines three categories of jets, as follows: pure jet, where the initial momentum is large and the buoyancy of the ambient fluid is small; volume flow, where the initial momentum is small and the buoyancy plays a dominant role; buoyancy jet, where there is certain initial momentum along with the effects from buoyancy [2]. Thermal jets are jets dominated by buoyancy and exhibit significant temperature differences compared to the surrounding fluids. For example, underwater vehicle thermal jets rely on circulating cooling systems for normal operation. The heat generated by these systems undergoes energy exchange before being discharged as high-temperature wastewater into surrounding water bodies. Advancements in infrared detection technology have improved environmental temperature change detection accuracy and reduced the risks of infrared detection for underwater vehicles. Therefore, studying the characteristics, such as formation, diffusion, and attenuation, and the laws governing buoyancy related to underwater thermal jets becomes crucial [3]. There are relevant studies in the literature to explain these problems [4; 5; 6; 7; 8; 9; 10; 11; 12]. During the process of thermal jet discharge, a strong doping heat transfer and thermal jet heat diffusion are produced between the thermal jet and the ambient water body [13]. Therefore, based on the development process of the thermal jet, it can be roughly divided into three regions, as follows: the pure jet region (dominated by initial momentum); the buoyant jet region (gradual weakening of initial momentum with increasing role of buoyancy force); and the volume flow stage (decreasing momentum attenuation with obvious role of buoyancy force). With advancements in laser detection methods, there has been a breakthrough in observing fluid motion. Techniques such as particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) have gained popularity due to their advantages in observability. The inclusion of marker particles in the jet reflects its flow field state, while velocity vectors are determined using pulsed light sources for particle scattering to measure flow fields [14; 15]. The actual ocean environment is characterized by a vertical gradient with spatially inhomogeneous seawater temperatures due to sunlight irradiation. Stable temperature stratification is often present within ocean interiors, leading to different temperature distributions across various ocean areas. The unevenness of seawater temperature, as well as the pressure and salinity variations, lead to a stratified vertical distribution of seawater density. This results in temperature differences between upper and lower layers of seawater, creating obvious temperature interfaces. [PERSON] [16] investigated the dynamics of forced plumes in linearly stable stratified environments by using PIV measurements, with a focus on turbulence and mixing behavior. Additionally, the response of jet outflow to influencing factors, such as outflow flow rate and depth of the jet in the water environment, were analyzed using the PIV technique for nonlinear stratified fluid environments [17]. Furthermore, [PERSON] [18] studied the flow characteristics and structure of highly buoyant jets entering stagnant high-density fluids utilizing scanning stereoscopic PIV combined with proper orthogonal decomposition (POD) analysis. The results indicated that the formation of jet vortex structures is induced by highly sheared layers between upper and lower velocities.