Abstract: Abstract: A hydrodynamic coupling has been one of the most important components for the driven machine using the flow of fluid. The internal flow field of the hydrodynamic coupling is characterized by an unsteady multi-scale eddy flow with multiple flow states and physical impacts. The overall flow inside depends mainly on the generation, development, and interaction of multi-scale vortices. It is necessary to finely characterize the unsteady multi-scale three-dimensional vortex structure inside the hydrodynamic coupling. In this study, a stress mixed eddy turbulence model was established to simulate the three-dimensional vortex flow field of the hydrodynamic coupling under the braking condition using computational fluid dynamics. A multi-scale analytical investigation was carried out to reveal the spatiotemporal evolution of the flow field and the mechanism of energy loss. Three types of vortex identification were used to extract the multi-scale vortex structure inside the turbine. The applicability of different vortex identification was analyzed from the perspective of spatial reconstruction, threshold selection range, and sensitivity. A Particle Image Velocimetry (PIV) flow field test was conducted to verify the accuracy and reliability of numerical simulation and vortex structure identification. Three-dimensional vortex structure characteristics and two-dimensional flow field maps were used to determine the temporal and spatial evolution of the turbulent flow inside the flow channel and the energy loss mechanism. The results show that there was a blind threshold selection in the Q criterion. Specifically, the structure extraction cannot concurrently capture both strong and weak vortex structures. There was also the incoherent structure of the vortex system, the insufficient reconstruction of the multi-scale vortex, and the missing vortex flow. As such, the Q criterion failed to accurately predict the continuous motion of the three-dimensional vortex space. By contrast, the Ω method captured the weak vortex structure within a large threshold range at the threshold of 0.51-0.59. Nevertheless, there were also no outstanding features of vortex structure extraction and the trend of vortex motion after the reconstruction of vortex system space. The ΩL method was not sensitive to the threshold selection, where the spatial vortex system refactoring performed the best when the threshold was 0.51-0.67. Correspondingly, the ΩL method can be expected to fully represent the structure characteristics of small-scale vortices and their movement trends. Strong and weak vortices can also be highly recognizable. Consequently, the overall flow inside the turbine can be defined as a large-scale counterclockwise circulation under braking conditions, accompanied by the local flow, such as the small-scale eddy currents. The mainstream vortex can be promoted by the vortex in the same direction, but hindered by that in the opposite. The fluid energy can be lost and dissipated in the form of heat energy, due to the tearing, crushing, separation, collision, friction, and extrusion of the vortex.