Conventional streamflow monitoring methods entail one-to-one relationships between two flow variables obtained by combining direct flow measurements with statistical analyses. These relationships (i.e. ratings) are used to monitor both steady and unsteady flows despite that in the latter cases the flow variables display an inherent hysteretic behaviour. Such behaviour is prominent if the wave passing through the gauging station is non-kinematic. This paper demonstrates that the index-velocity and continuous slope-area methods are more suitable to monitor unsteady flows in comparison with the widely used stage–discharge approach. Case studies are presented to show that, contrary to current perceptions in practical applications, hysteresis can be captured even in small streams and frequently-occurring run-off events. The paper also highlights the separation of the flow variable hydrographs in unsteady flows. This hysteresis-related aspect is less investigated so far despite having important practical implications for both hydrometric and fluvial transport applications.

The dynamics of coherent structures forming in a turbulent shallow mixing layer (ML) between two parallel streams advancing in a constant-depth, open channel is investigated using three-dimensional, time-accurate simulations. The large channel length to flow depth ratio () allows characterization of the spatial evolution of shallow MLs until the mean velocity difference between the two streams becomes less than 3% of the initial value at the end of the splitter plate. Away from the ML origin, the dynamics and coherence of the Kelvin–Helmholtz (KH) billows are affected by the destabilizing effect of the mean shear between the two streams and by the stabilizing effect of the bed friction. A linear decay of the entrainment coefficient α with the bed-friction factor, S, applies only over the region where merging of neighbouring KH billows is still observed (transition to quasi-equilibrium regime). At larger distances from the origin, where the billows are severely stretched in the streamwise direction before being destroyed, the rates of increase of the ML width, δ, and centreline shift, lcy, become very small and α is exponentially decaying with increasing S toward zero (quasi-equilibrium regime). During the initial stages of the quasi-equilibrium regime where the KH vortices are severely stretched, the ML assumes an undulatory shape in horizontal planes. New relationships are proposed to characterize the downstream variation of the non-dimensional ML width and centreline shift over the transition and quasi-equilibrium regimes. During the transition to equilibrium regime, the ML boundary on the fast-stream side remains close to vertical, while that on the slow-stream side becomes strongly tilted. The ML boundary on the slow-stream side becomes again close to vertical once the quasi-equilibrium regime is reached. During the transition to the equilibrium regime, the passage of the KH billows and the generation of streamwise cells of secondary flow generate regions of high instantaneous bed shear stress, such that the region where the erosive capacity of the flow peaks does not correspond to the fast stream. The paper also investigates the effects of flow shallowness and initial velocity ratio between the two streams on the turbulent kinetic energy inside the ML, the depth-averaged lateral momentum fluxes, the passage frequency and size of the KH billows and the wavelength and period of the undulatory motions of the ML during the early stages of the quasi-equilibrium regime.

When two converging flows of unequal velocities and different flow directions come into contact, large-scale coherent structures are generated. For shallow conditions and small angles between the incoming streams, the mixing layer (ML) forming downstream of the confluence apex contains quasi-two-dimensional, Kelvin–Helmholtz (KH) vortices. Due to flow shallowness (e.g. stabilizing effect of bed friction), these vortices gradually lose their coherence at large distances from the ML origin. For large angles between the incoming streams, the spatial development of the shallow ML is more complex as strongly coherent, streamwise-oriented-vortical (SOV) cells form in the vicinity of the shallow ML and helical cells of secondary flow are generated due to curvature effects. The present paper uses three-dimensional eddy-resolving numerical simulations to study the effects of varying the angles between the two incoming channels and the downstream channel, the velocity ratio (VR) of the incoming flows and the flow depth on flow, turbulence structure and sediment entrainment mechanisms inside the ML and its surroundings. The simulations are performed for highly idealized conditions in which the ML develops in a wide channel (no interactions with the channel banks), over a flat bed and the flow depth is constant. Simulation results show that the SOV cells play an important role in the redistribution of the streamwise momentum. Some of the SOV cells are subject to bimodal oscillations in the lateral direction which induce strong interactions between the SOV cells and the ML vortices and sharply increase mixing. As for the case of a shallow ML developing between parallel streams, vortex pairing ceases some distance from the ML origin, the KH vortices start losing their coherence and the ML assumes an undulatory shape. The paper describes the effects of VR, angle between the incoming streams (α = 0° and 60°), planform geometry (symmetric vs. asymmetric confluences with α = 60°) and flow shallowness on the transverse shift of the ML centreline, ML width, dynamics of the KH vortices and on the formation, position and circulation of the SOV cells. In most of the α = 60° cases, the largest bed shear stresses are induced beneath the SOV cells rather than beneath the high-speed stream and the SOV cells play a major role in enhancing mixing between the two streams.