Turner angle is usually discussed when researching ocean stratification and double diffusion.
Turner angle assesses the vertical stability, indicating the density of the water column changes with depth. The density is generally related to potential temperature and salinity profile: the cooler and saltier the water is, the denser it is. As the light water overlays on the dense water, the water column is called stable stratification. The buoyancy force preserves stable stratification. One characteristic of stability is that the Brunt-Vaisala frequency N>0, which includes three situations of doubly stable, thermal diffusion, and salt fingering. Considering the density attribute to both temperature and salinity, a "double stable" status, where the temperature decreases with depth (∂θ/∂z>0) and salinity increases with depth (∂S/∂z<0), is the most ideal stable water column, which means the water column is stably stratified with respect to both θ and S.
The water column can maintain stability even though one attribute does not agree. In one case of heat diffusion dominant, diffusive double-diffusion is possible when the salinity structure is stable while the temperature structure is unstable (∂θ/∂z<0, ∂S/∂z<0). In the other case, salt fingering can be expected when relatively warm, salty water overlies relatively colder, fresher water (∂θ/∂z>0, ∂S/∂z>0). Both these cases lead to turbulence and mixing on the vertical structure of the water column.
Since Turner angle can indicate the thermal and haline properties of the water column, it is used to discuss water thermal and haline structures,  and demonstrated benefits of localizing the boundaries of the subarctic front.