We numerically study the displacement flow of two iso-viscous Newtonian fluids in an inclined two-dimensional channel, formed by two parallel plates. The results are complementary to our previous studies on displacement flows in pipes and channels. The heavier displacing fluid moves the lighter displaced fluid in the downward direction. Three dimensionless groups largely describe these flows: the densimetric Froude number (Fr), the Reynolds number (Re), and the duct inclination (β). As a first order approximation, we are able to classify different flow regimes phenomenologically in a two-dimensional (Fr; Recosβ/Fr)-plane and provide leading order expressions for the transitions between different regimes. The stabilizing and/or de-stabilizing effects of the imposed mean flow on buoyant exchange flows (zero imposed velocity) are described for a broad range of dimensionless parameters.
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