Flows Over Flexible Vegetation Canopies: Hydrodynamic Impact and Drag Modeling

In the field of environmental fluid mechanics, flows over vegetated canopies remain a critical research area. Vegetation covering natural watercourse beds significantly influences flow hydrodynamics, turbulence structures (Nepf & Vivoni 2000, Luhar et al. 2008), sediment transport (Morris et al. 2008), and hydraulic efficiency (Nikora 2008). Furthermore, it impacts aquatic habitats (Wilcock 1999) and water quality (Chambers & Prepas 1994). Despite extensive studies, the influence of highly flexible and elongated vegetation morphologies, such as seagrass and water ranunculus, remains poorly understood.

The primary objective of this study is to investigate the influence of highly interactive vegetation structures on velocity profiles, turbulent stress tensors, and drag, in comparison with rigid, less flexible, or less elongated canopies. A secondary objective is to propose a generalized friction law for this type of canopy.

To model this vegetation, we constructed a synthetic bed using rectangular plastic bands (1 cm wide, 29.8 cm long, 𝐸𝐼=1.5×10−6 MPa). Experiments were conducted in a tiltable flume (4 m long, 40 cm wide) at the IMFT laboratory in Toulouse. A total of 24 uniform and stationary turbulent flows were analyzed under various hydraulic regimes, alongside vegetation image analysis. Accurate flow velocity measurements were obtained for 7 uniform regimes using Particle Image Velocimetry (PIV). Spatio-temporal double-averaged decomposition of the turbulent field (Nikora 2007) was employed to estimate mean turbulent profiles, including Reynolds stress tensors, and to calculate vertical drag profiles from the momentum equation.

The vegetation bands exhibited bending near the bed (wake zone) and flapping motions further up (flapping zone), driven by turbulence. The highly elongated canopy flow demonstrated a bi-layer structure, with distinct vertical distributions of drag and turbulent stresses corresponding to each zone’s characteristic length scale. From the observed vegetation structure and drag profiles, we developed physically based drag laws for both the wake and flapping zones. By coupling these drag laws with the universal logarithmic law for flow for the outer flow, we derived a Darcy friction law for flow over dense, submerged, and highly elongated flexible canopies.