On the solidity parameter in canopy flows

Abstract

We have performed high-fidelity simulations of turbulent open-channel flows over submerged rigid canopies made of cylindrical filaments of fixed length $l=0.25H$ ( $H$ being the domain depth) mounted on the wall with angle of inclination $\theta$ . The inclination is the free parameter that sets the density of the canopy by varying its frontal area. The density of the canopy, based on the solidity parameter $\lambda$ , is a widely accepted criterion defining the ongoing canopy flow regime, with low values ( $\lambda \ll 0.1$ ) indicating the sparse regime, and higher values ( $\lambda > 0.1$ ) the dense regime. All the numerical predictions have been obtained considering the same nominal bulk Reynolds number (i.e. $Re_b=U_b H/\nu = 6000$ ). We consider nine configurations of canopies, with $\theta$ varying symmetrically around $0^{\circ }$ in the range $\theta \in [\pm 78.5^{\circ }$ ], where positive angles define canopies inclined in the flow direction (with the grain) and $\theta =0^{\circ }$ corresponds to the wall-normally mounted canopy. The study compares canopies with identical solidity obtained inclining the filaments in opposite angles, and assesses the efficacy of the solidity as a representative parameter. It is found that when the canopy is inclined, the actual flow regime differs substantially from the one of a straight canopy that shares the same solidity, indicating that criteria based solely on this parameter are not robust. Finally, a new phenomenological model describing the interaction between the coherent structures populating the canopy region and the outer flow is given.