To cite this version:V. Dupuis, S. Proust, C. Berni, A. Paquier. Mixing layer development in compound channel flows with submerged and emergent rigid vegetation over the floodplains. Experiments in Fluids, Springer Verlag (Germany), 2017, 58 (4), pp.30. <10.1007/s00348-017-2319-9>. Author-produced version of the article published in Experiments in Fluids, 2017 The original publication is available at http://link.springer.com/article/10.1007/s00348-017-2319-9 DOI: 10.1007/s00348-017-2319-9Mixing layer development in compound channel flows with submerged and emergent rigid vegetation over the floodplains Victor Dupuis · Sébastien Proust · Céline Berni · André Paquier Received: date / Accepted: date Abstract This laboratory study aims at investigating the longitudinal development of a mixing layer in a compound open-channel (two-stage geometry with a main channel and adjacent floodplains). The floodplains are covered with two roughness types: either a bed roughness representing a submerged dense meadow or emergent roughness elements (cylinders) representing an alluvial forest. The theoretical background used for plane mixing layers is adapted to the highly threedimensional mixing layer that develops at the main channel/floodplain interface. The mixing layer width is divided into two parts on either side of the interface. For the wooded floodplain, the mixing layer width on the floodplain side levels off downstream much more rapidly than for the grassed floodplain. The lateral profiles of normalised velocity and turbulence quantities are found to be self-similar in the longitudinal direction for a fixed elevation. However, shallowness effects prevented the normalised lateral profiles of velocity and turbulence quantities from coinciding at different elevations. The respective contributions of lateral Reynolds stresses and secondary currents to the lateral exchange of momentum are estimated. At the main channel/floodplain interface, the momentum exchange is driven by Reynolds stresses. In the main channel, both Reynolds stresses and secondary currents contribute to the lateral flux of momentum. Secondary cur-

Open channel flows subjected to a longitudinal transition in roughness, from bed friction to emergent cylinder drag and vice versa, are investigated experimentally in an 18 m long laboratory flume. These are compared to uniform flows subject to (1) bed roughness only and (2) an array of emergent vertical cylinders installed on bed roughness. The nearbed region is investigated in detail for uniform flows through the cylinder array. The water column can be divided into two parts: a region of constant velocity and a boundary layer near the channel bed. In the latter region, a local increase in velocity, or velocity bulge, is observed in line of a cylinder row. The velocity bulge may be related to the disorganization of the von Kármán vortex street by the bed-induced turbulence, resulting in reduced momentum loss in the cylinder wake. The boundary layer height is found to be independent of water depth and bed roughness (smooth or rough bottom). Strong oscillations of the free surface (seiching) are observed. Oscillation amplitude is dependent on the longitudinal position within the cylinder array and is found to decrease with decreasing array length. When water depth/boundary layer height ratio is close to unity, the disorganization of the von Kármán vortex street throughout the water column prevents seiching from occurring. In the case of roughness transition flows, the water depth is found to vary only upstream of the change in roughness. Vertical profiles of velocity and turbulence are self-similar upstream of the transition and collapse with the uniform flow profiles. Downstream of the roughness change, velocity and turbulence vary over a distance of 35 to 50 times the water depth. Roughness transition flows show that seiching is lowered by flow non-uniformity. A 1D momentum equation integrating bed friction and drag force exerted by the cylinder array predicts accurately the water surface profile (0.9 % mean relative error). The computed profiles show that, upstream of the transition, flow depth varies over a distance of about 2600 times the uniform water depth of the upstream roughness. The 1D equation is solved analytically for zero bed friction.

Transitions from submerged dense vegetation (meadow) to emergent rigid vegetation (wood) and vice versa are modelled using plastic grass and vertical wooden cylinders. For a given roughness transition, the upstream discharge distribution between main channel and floodplain (called subsections) is also varied, keeping the total flow rate constant. The flows with a roughness transition are compared to flows with a uniformly distributed roughness over the whole length of the flume. Besides the influence of the downstream boundary condition, the longitudinal profiles of water depth are controlled by the upstream discharge distribution. The latter also strongly influences the magnitude of the lateral net mass exchanges between subsections, especially upstream from the roughness transition. Irrespective of flow conditions, the inflection point in the mean velocity profile across the mixing layer is always observed at the interface between subsections. The longitudinal velocity at the main channel/floodplain interface, denoted U int , appeared to be a key parameter for characterising the flows. First, the mean velocity profiles across the mixing layer, normalised using U int , are superimposed irrespective of downstream position, flow depth, floodplain roughness type and lateral mass transfers. However, the profiles of turbulence quantities do not coincide, indicating that the flows are not fully self-similar and that the eddy viscosity assumption is not valid in this case. Second, the depth-averaged turbulent intensities and Reynolds stresses, when scaled by the depth-averaged velocity U d,int exhibit two plateau values, each related to a roughness type, meadow or wood. Lastly, the same results hold when scaling by U d,int the depth-averaged lateral flux of momentum due to secondary currents. Turbulence production and magnitude of secondary currents are increased by the presence of emergent rigid elements over the floodplains. The autocorrelation functions show that the length of the coherent structures scales with the mixing layer width for all flow cases. It is suggested that coherent structures tend to a state where the magnitude of velocity fluctuations (of both horizontal vortices and secondary currents) and the spatial extension of the structures are in equilibrium.

Flow experiments are conducted in a two-stage compound open-channel, with varying intensity of the velocity difference between the main channel (deep part) and the floodplain (shallower part), using a large-scale free surface PIV technique (LS-PIV). For all investigated flows, a shear layer develops at the interface between main channel and floodplain, characterised by a peak of turbulent shear stress. Yet, two different kinds of shear layer could be identified. The first kind is characterised by the presence of large-scale quasi-periodic structures of Kelvin-Helmholtz type which are growing in downstream direction, whereas the second kind is characterised by smaller-scale vortical structures without quasi-periodicity and which do not grow in downstream direction. The shear parameter $$\lambda =(U_2-U_1)/(U_2+U_1)$$ λ = ( U 2 - U 1 ) / ( U 2 + U 1 ) , where $$U_1$$ U 1 and $$U_2$$ U 2 are defined as the velocities outside the shear layer, is identified as a key parameter to distinguish between these two types of shear layers, supporting a result from Proust et al. (Water Resour Res 53: 3387–3406, 2017). A physical interpretation of the $$\lambda$$ λ -criterion is proposed, based on the inhibiting effect of ambient turbulence (the turbulence level outside the shear layer) on the emergence of Kelvin-Helmholtz structures. Accordingly, the threshold value of $$\lambda$$ λ , above which large-scale structures can develop, is dependent on the level of the ambient turbulence. Despite their very different behaviours, the two types of shear layer have the same efficiency to generate turbulent shear stress for a given velocity difference across the shear layer, except for $$\lambda$$ λ -values close to the threshold value.

River beds frequently exhibit a lateral variation of roughness. For example, in the case of an overflowing river, the main channel has a smoother topography compared to the adjacent floodplains where vegetation and land occupation yield an important hydraulic roughness. The lateral difference in roughness can induce a high lateral velocity gradient within the river cross- section that gives birth to a mixing layer. This mixing layer leads to fluid and momentum transfers between the two adjacent beds. To understand such mix- ing processes in rivers is important for predicting stage-discharge relationships and the velocity distribution within the cross-section. In order to address these issues in the context of a shallow water flow with a water depth h of the same order as the roughness elements of the bed, experiments were undertaken in a 26 m long and 1.1 m wide glass-walled open-channel flume. One half-side of the bed was covered with an array of cubes of height k arranged in a square configuration, the other side with smooth glass. Three different levels of cube submergence h/k were examined (h/k = 0.8, 1.5 and 2). The experiments and measurements were designed to yield the flow in the complete volume of the interstices across the cube array. To achieve this, 2C-3D linear-scanning PIV measurements with zero-parallax optics were developed and set up. The mea- surements revealed the complexity of the flow structure around the interface between the rough and smooth beds. The results show that the ability of the mixing layer to exchange momentum is highly dependent on the level of the cube submergence h/k.