Turbidity currents (TCs) are a common kind of particle-laden flow in underwater natural environments. This work employs a Eulerian–Lagrangian model to investigate the dynamic regimes of lock-exchange TC in a moderate flow Reynolds number range (${Re} = 1716-3836$) as well as the formation and evolution mechanisms of interfacial Kelvin–Helmholtz (KH) billows composed of a fluid–particle mixture. The results demonstrate that a fluid streak with high stretching at the interface, which twists and takes on a braided structure, is the key to the onset of KH instability. An increase in ${\textit{Re}}$ results in a higher interfacial fluid velocity gradient that intensifies the shear instability, and an increase in the convergent fluid force acting on the particles. This provides an explanation for the significant increases both in quantity and strength of KH vortices as ${\textit{Re}}$ rises. The enhanced KH vortices contribute to particle suspension and streamwise transport at larger ${\textit{Re}}$, leading to an extension in the duration of the slumping stage, which exhibits a constant forward velocity regime. The spatially continuous braided structure in the vorticity sheet region is responsible for the intriguing merging phenomenon of interfacial vortices. Furthermore, TC kinetic energy increases with the increasing ${\textit{Re}}$, and the system dissipation rate decreases in the early and middle stages of the TC. This behaviour may be correlated to the reducing shear between the TC and ambient fluid by interfacial KH billows. Regarding the turbulent kinetic energy dissipation of interfacial vortices, normal strain predominates in the middle stage, while shear deformation is most prevalent in the early and later stages.