Wave-like motion and secondary currents in arrays of emergent cylinders induced by large scale eddying motion

Free-surface flows with riparian corridors are known to develop large eddies resulting from the instability associated to the inflectional profile of the longitudinal velocity in the spanwise direction. They periodically generate strong momentum exchanges inside the vegetation corridor, triggering a wave-like motion, detectable as free-surface oscillations and out-of-phase velocity components. We propose a characterization of the flow inside the vegetation corridor, focusing on the wave-like motion and its influence on secondary currents. We conditionally sample the fluid motion to highlight the structure of the phase-averaged coherent structure. Quadrant analysis shows that there is a strong variation of Reynolds stress anisotropy in the spanwise direction, which is one of the key generation mechanisms of secondary currents. Spectrograms of longitudinal and lateral velocity fluctuations reveal that the oscillatory motion is imposed on the whole of the vegetated layer, because of continuity. The analysis of the phase-averaged 2D vertical-longitudinal flow reveals that there is a complex 3D pattern of mass fluxes associated to each large eddy. In particular there is an anti-symmetric net mass imbalance which, by mass conservation, generates a mass flux directed outwards, to the main channel, near the bottom of the channel. The Eulerian expression of this motion is obtained as the spatial average of the flow over the length of the large eddy, resulting in the pattern of the secondary current in the vertical-spanwise plane. It is shown that the secondary motion is a necessary feature of free-surface turbulent flows that develop large-scale inflectional instabilities. Article highlights The flow presents a marked anisotropy in the core of the large-scale eddies resulting from high shear stress associated with the passage of this, and the spanwise variation of Reynolds stress anisotropy is related to the formation and growth of secondary flow. Analysis of the phase-averaged 2D vertical-longitudinal flow revealed that there is a complex 3D pattern of mass fluxes associated to large eddy, and by spatially-averaging this flow along the length of the eddy, it is obtained the Eulerian vertical-spanwise velocity field where the secondary currents are visible. A deterministic model of streamlines trends is proposed, based on the continuity equation, which explains the secondary current as a function of inflectional instability.