Abstract: Stably stratified shear flows are ubiquitous in environmental and geophysical settings. The dynamics of such flows involve a competing interaction between (stabilising) density stratification and (destabilising) background shear. Stratified turbulence is often localised in space-time particularly when the effects of stable density stratifications are strong. However, stratified turbulence can be affected dramatically by non-local effects such as internal hydraulics or wall-generated inhomogeneity. In this talk, I’ll discuss mainly the internal hydraulic effects on the evolution of the stratified inclined duct (SID) as the first test problem. The dynamics are interpreted in terms of the propagation of information (characteristics) of the two and three-layer hydraulic model and the instability of long waves in the system. The effects of spanwise confinement and variation of Prandtl numbers on the location of hydraulic control points and hydraulic flow regimes are addressed and discussed.  The role of inhomogeneity on the non-locality of stratified shear-driven turbulence is presented in stratified open channels as the second test problem. The energy density with a full band of horizontal and vertical scales is then investigated in detail to reveal the significance of inhomogeneity through inner and outer layer interactions.