Stratified shear flow in an inclined square duct

We present results of experiments on stratified shear flow in an inclined duct. The duct connects two reservoirs of fluid with different densities, which drives a counterflow with a dense layer flowing beneath a less-dense layer moving in the opposite direction. Depending on the dimensionless Atwood number $A$ and duct angle $\theta$, we identify four flow states: a laminar $\mathsf{L}$ state, a Holmboe wavemode $\mathsf{H}$ state, a spatio-temporally intermittent $\mathsf{I}$ state, and a fully developed turbulent $\mathsf{T}$ state. We map a state diagram of these flows in the Atwood number -- $\theta$ plane and examine the force balances that determine each of these states. We find the $\mathsf{L}$ and $\mathsf{H}$ states to be hydraulically controlled at the ends of the duct and the flow is determined by the pressure difference associated with the density difference between the reservoirs. The $\mathsf{I}$ and $\mathsf{T}$ states are associated with increasing dissipation within the duct. We replot the state-space in the Grashof number -- $\theta$ phase plane and find the transition to the $\mathsf{T}$-state is governed by a critical Grashof number. We then evaluate the level of turbulence by examining scalings for the thickness of interfacial region between the two layers.