## 1 Introduction  
The supersonic mixing layer is a common compressible turbulent flow, which exists in supersonic ejectors and combined cycle engines. Taking a rocket-based combined cycle engine (RBCC) as an example, the gas emitted by the rocket engine and the supersonic air compressed by the inlet must be mixed and burned in a very short time [1]. The mixing degree of gas and air in the combustion chamber directly affects the performance of the engine. Therefore, an in-depth study of the supersonic mixing layer is beneficial for improving the performance of the engine, and it is of great significance in understanding the mechanism of supersonic turbulent flow. Research on the supersonic mixing layer began in the 1970s and 1980s. In 1988, [PERSON] and [PERSON] [2] studied supersonic-supersonic and subsonic-supersonic laminar mixing flow fields with nitrogen, helium, and argon as working fluids, developing [PERSON]'s theory [3], and proposed the concept of convective Mach number. Convective Mach number is derived from the relative motion of large-scale structure and free flow in the mixing layer, which is an important parameter in characterizing the compressible effect of the mixing layer. Studies [4] have shown that an increase in the convective Mach number has an inhibitory effect on the growth of the mixing layer. The reason is that the increase of convective the Mach number causes two-dimensional and large-scale structures in the mixing layer to produce spanwise disturbance and transform into an irregular three-dimensional structure [5; 6; 7], thereby reducing the ability of the mixing layer to entrain and merge the surrounding fluid. However, there is also a critical value in the range of 0.5-1 for the influence of the convective Mach number on the growth rate of the mixing layer [8; 9]. When the convective Mach number is greater than the critical value, the growth rate of the mixing layer reaches a minimum and remains unchanged [10]. The development of the supersonic mixing layer can also be affected by pressure, velocity, density, and other factors. The mismatched pressure of the primary and secondary flow can change the transition position of the mixing layer and the development of a large-scale vortex structure, and also make the mixing layer tilt to the low-pressure side, inhibiting the growth of the mixing layer [11]. [PERSON] compared the mixed layer flow with pressure ratios of 1.0, 1.5, and 2.0, and found that a pressure ratio of 2.0 had the most obvious inhibitory effect on the mixed layer [12]. The effect of velocity ratio was similar to that of the convective Mach number, that is, an increase of velocity ratio could inhibit the development of the mixing layer, and the density ratio had no significant effect on the development of the mixing layer [13]. In addition, the geometric size of the mixing layer flow channel and the shape of the separator are important factors affecting the development of the mixed layer. Reasonable adjustment of the contraction and expansion angle and length of the combustion chamber enhance mixing. Special-shaped baffles (Figure 1), such as serrated and lobed baffles, are also used to enhance the mixing of the mixing layer, among which use of a lobed baffle is currently recognized as the most effective method [14]. Measurement techniques for the supersonic mixing layer are also developing. The measurement methods based on a pitot tube and a total static pressure sensor were often used in early studies [1,16]. [PERSON] et al. [4] measured the velocity distribution of the supersonic mixing layer flow in the range of convective Mach numbers from 0.4-1.97, velocity ratios of 0.16-0.79, and density ratios of 0.57-1.55, with an LDV (Laser Doppler Velocimetry), and developed similarity profiles of normalized velocity at different working conditions and different locations, which have served as reference measurements for verification of many experimental and numerical studies. [PERSON] et al.