  Buoyancy-driven exchange flows arise in the natural and built environment
wherever bodies of fluids at different densities are connected by a narrow
constriction. In this paper we study these flows in the laboratory using the
canonical stratified inclined duct experiment, which sustains an exchange flow
in an inclined duct of rectangular cross-section over long time periods (Meyer
& Linden, J. Fluid Mech., vol. 753, 2014). We study the behaviour of these
sustained stratified shear flows by focusing on three dependent variables of
particular interest: the qualitative flow regime (laminar, wavy, intermittently
turbulent, or fully turbulent), the mass flux (net transport of buoyancy
between reservoirs), and the interfacial thickness (thickness of the layer of
intermediate density between the two counter-flowing layers). Dimensional
analysis reveals five non-dimensional independent input parameters: the duct
aspect ratios in the longitudinal direction $A$ and spanwise direction $B$, the
tilt angle $\theta$, the Reynolds number $Re$ (based on the initial buoyancy
difference driving the flow), and the Prandtl number $Pr$ (we consider both
salt and temperature stratifications). After reviewing the literature and open
questions on the scaling of regimes, mass flux, and interfacial thickness with
$A,B,\theta,Re,Pr$, we present the first extensive, unified set of experimental
data where we varied systematically all five input parameters and measured all
three output variables with the same methodology. Our results in the
$(\theta,Re)$ plane for five sets of $(A,B,Pr)$ reveal a variety of scaling
laws, and a non-trivial dependence of all three variables on all five
parameters, in addition to a sixth elusive parameter. We further develop three
classes of candidate models to explain the observed scaling laws: ...
