Shear-layer turbulence and drag in submerged flexible canopies with lateral sway

Submerged vegetated canopies generate a canopy-top shear layer that governs vertical momentum exchange, turbulence production, and hydraulic resistance. While flexibility-driven streamwise reconfiguration has been widely studied, the incremental role of lateral sway—spanwise stem motion superimposed on the nominally streamwise shear layer—remains poorly constrained. Lateral-sway effects are isolated using a paired numerical design: for each flexibility level (Cauchy number Ca = 15–75, spanning weak to strong flow-induced reconfiguration), otherwise identical, fully developed open-channel canopy flows are simulated with either streamwise-only stem motion or fully three-dimensional motion including spanwise sway. The simulations resolve unsteady eddies and stem-scale loading through two-way coupling between the flow and a nonlinear beam model of flexible stems, enabling dynamic canopy–flow interaction without empirical drag tuning. Mixing-layer measures characterize the exchange-layer location and thickness using the interior–overflow velocity contrast, and double-averaged momentum budgets separate turbulence-driven (Reynolds) and form-induced contributions. Increasing flexibility reduces the effective canopy height by about 30%–33% and thickens the exchange layer, with Reynolds-stress influence becoming nearly depth filling by Ca ≈ 50. Allowing lateral sway increases resistance, raising array-integrated drag by about 14%–18% and reducing pore and overflow velocities at matched Ca. This resistance increase is associated with realized spanwise tip excursions, which increase time-varying projected exposure and motion-induced momentum extraction near the canopy–overflow interface, limiting overflow acceleration even as mean reconfiguration reduces blockage. Lateral sway leaves the depth reach of Reynolds-stress penetration largely unchanged but reorganizes the transport pathway: spanwise meandering weakens the persistence of canopy-locked wake/jet structures, suppresses form-induced momentum flux within the canopy, and shifts stress support toward turbulence. Consistent with the mean-flow response, sway shifts the most active exchange region closer to the vegetation, strengthening canopy-side turbulence relative to the overflow. Coherence measures therefore respond more strongly than penetration measures, indicating a decoupling between the depth reach of interfacial influence and the organization of momentum transport. These findings identify when lateral sway should be represented, or parameterized, to predict shear-layer turbulence, momentum exchange, and drag scaling in submerged flexible-canopy flows.