# Stratiﬁed shear ﬂow: experiments in an inclined duct

Article

We present results of experiments on stratiﬁed shear ﬂow in an inclined duct. The duct connects two reservoirs of ﬂuid with different densities, and contains a counterﬂow with a dense layer ﬂowing beneath a less-dense layer moving in the opposite direction. We identify four ﬂow states in this experiment, depending on the fractional density differences, characterised by the dimensionless Atwood number, and the angle of inclination θ, which is deﬁned to be positive (negative) when the along-duct component of gravity reinforces (opposes) the buoyancy-induced pressure differences across the ends of the duct. For sufﬁciently negative angles and small fractional density differences the ﬂow is observed to be laminar (L state) with an undisturbed density interface separating the two layers. For positive angles and/or high fractional density differences three other states are observed. For small angles of inclination the ﬂow is wave-dominated and exhibits Holmboe modes (H state) on the interface with characteristic cusp-like wave breaking. At the highest positive angles and density differences there is a turbulent (T state) high-dissipation interfacial region typically containing Kelvin-Helmholtz (KH)-like structures sheared in the direction of the mean shear and connecting both layers. For intermediate angles and density differences an intermittent state (I state) is found, which exhibits a rich range of spatio-temporal behaviour and an interfacial region that contains features of KH-like structures and of the other two lower-dissipation states: thin interfaces and Holmboe-like structures. We map the state diagram of these ﬂows in the Atwood number – θ plane and examine the force balances that determine each of these states. We ﬁnd that the L and H states are 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. As the inclination increases, the along-slope component of the buoyancy force becomes more signiﬁcant and the I and T states are associated with increasing dissipation within the duct. We replot the state-space in the Grashof number – θ phase plane and ﬁnd the transition to the T-state is governed by a critical Grashof number. We ﬁnd that the corresponding buoyancy Reynolds number of the transition to the T-state is of order 100, and that this state is also found to be hydraulically controlled at the ends of the duct. In this state the dissipation balances the force associated with the along-slope component of buoyancy and the counterﬂow has a critical composite Froude number.