###### Abstract  
In modern turbine rotors, tip-leakage flow is a common phenomenon that accounts for about 1/3 of the stage loss. Studies show that as the imposed load increases, a shock wave appears in the tip region, which causes a significant interference on the leakage vortex. In the present study, numerical simulations are carried out to investigate the influence of the shock wave on the loss and breakdown of the tip-leakage vortex. The obtained results indicate that with no effective control on the flow, the loss of the leakage vortex has an approximate exponential growth up to about 10 times as the outlet Mach number increases from 0.67 to 1.15 and the corresponding proportion in the total loss increases sharply to 30.2%. It is found that the stagnation position of the breakdown changes with the backpressure and the amplitude of variation along the axial direction is up to 0.13 C\({}_{\rm x}\). It is inferred that the breakdown of the leakage vortex core may be affected by the periodical passing of downstream blade and the induced pressure fluctuation may result in additional vibration in this rotor blade. The leakage vortex is unstable in supersonic flow with a shock wave and it may transfer to a flow with a low-velocity bubble in its core region. It is concluded that the leakage vortex breakdown mainly originates from interferences of the shock wave, while the internal cause of such breakdown is the centrifugal instability of the vortex. tip-leakage loss; vortex breakdown; shock wave/vortex interaction; vortex instability 2021114991 202114991 it was found that the loss core separation in the positive suction corner pressure gradient may rapidly increase the size of the tip-leakage vortex. However, further investigations are required in this regard. [PERSON] et al. [7] used the long-wave instability theory and analyzed the stability of the turbine tip-leakage vortex and found that the leakage vortex is unstable. Moreover, [PERSON] [8,9] and [PERSON] et al. [10] showed that the mixing loss after the vortex breaking is an important source of leakage flow. They revealed that when the leakage vortex breakdown occurs, the mixing loss significantly increases and the scraping effect originating from the relative movement of the casing wall has a great effect on the instability and loss of the tip-leakage vortex [11]. The phenomenon indicates that the unsteady tip-leakage vortex is a very important parameter to control aerodynamic losses in the turbine rotor. On the other hand, a significant increase in the aerodynamic load of the turbine leads to the application of transonic turbine design. In addition, the shock wave structure near the trailing edge is one of the main flow characteristics of the transonic turbine. This feature is especially more pronounced in the rotor tip region. The turbine trailing-edge shock wave causes a sharp drop in the aerodynamic efficiency and may cause numerous problems such as blade vibration and flow unsteadiness. Consequently, the interaction between the shock wave and the blade, including the shock wave/boundary layer interaction [12,13] and the shock wave interaction with downstream blade row [14,15], have been comprehensively studied in recent years. However, the majority of these studies are focused on two-dimensional (2D) or quasi-two-dimensional flows and few investigations have been focused on the interaction between the shock wave and three-dimensional (3D) flows, such as the turbine endwall secondary flow, the tip-leakage flow/vortex and other 3D flows. Shock wave may cause a strong quasi discontinuity with a significant pressure gradient between flows at two sides. When the shock wave appears in the rotor tip region, the tip-leakage flow may be significantly affected. Since the tip leakage of a compressor is related to the compressor's operating margin, the interaction of compressor tip leakage vortex and shock wave has been widely studied as far [16, 17, 18, 19]. However, the turbine does not have an operating instability problem.