On the solidity parameter in canopy flows

TL;DR

This study uses high-fidelity simulations to examine how the solidity parameter influences flow regimes over inclined canopies, revealing that inclination significantly affects flow behavior beyond what solidity alone predicts.

Contribution

It introduces a new phenomenological model for canopy-flow interactions and questions the robustness of the solidity parameter as a sole flow regime criterion.

Findings

Inclined canopies exhibit different flow regimes than straight ones with the same solidity.

The solidity parameter alone is insufficient to predict flow regimes in inclined canopies.

A new model describes interactions between canopy structures and outer flow.

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 an 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 $0{\deg}$ in the range $\theta\in [\pm 78.5{\deg}]$, where positive angles define canopies inclined in the flow direction (with the grain) and $\theta=0{\deg}$ 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 solely based 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.