The Thorpe length $L_T$ is an efficient quantity that measures the extent of overturning in stably stratified flows because it only requires a determination of the density field whereas other length scales require information about the velocity field. Thus, $L_T$ is of great interest in oceanography where access to, for example, turbulent energy dissipation is challenging. We use experimental data from a wall-bounded shear flow, similar in nature to an oceanic overflow such as the Mediterranean outflow, to evaluate the stability and mixing characteristics of stably-stratified turbulent shear flows over a range of gradient Richardson number $\mathit{Ri}_g$ from 0.1 to 1. The flow is confined from the top by a transparent horizontal boundary and a lighter fluid is injected into quiescent heavier fluid with relative density difference between 0.0026 and 0.0052. The flow near the boundary is turbulent with a Taylor Reynolds number $R_\lambda \approx 100$, and the density and velocity fields are measured simultaneously using planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV). \\ \\

The Thorpe length $L_T$ is the root-mean-square average of Thorpe displacements which are defined as the displacements parallel to gravity necessary to transform a non-monotonic (gravitationally unstable) profile into a monotonic (stable) profile. We evaluate $L_T$ at different downstream positions along the interface between the turbulent current and the quiescent fluid. As $\mathit{Ri}_g$ increases from 0.1 to 1, the interface fraction with non-vanishing $L_T$, i.e., overturning, varies from near 1 to near 0 and the character of the interfacial instability changes from Kelvin--Helmholtz to Holmboe type. Despite the different nature of the interfacial instability, the probability distribution of the normalized non-zero values of Thorpe length, $(L_T-$\langle L_T\rangle)/\sigma(L_T)$ (non-zero average $\langle L_T\rangle$ and standard deviation $\sigma(L_T)$) has universal exponential tails. We also compare the characteristics of $L_T$ with the Ozmidov length $L_O$ and the Ellison length $L_E$ and evaluate the buoyancy Reynolds number $\mathit{Re}_b$.