Universal scaling-law for flow resistance over canopies with complex morphology

Simonetta Rubol,Bowen Ling,Ilenia Battiato

doi:10.1038/s41598-018-22346-1

Abstract

Flow resistance caused by vegetation is a key parameter to properly assess flood management and river restoration. However, quantifying the friction factor or any of its alternative metrics, e.g. the drag coefficient, in canopies with complex geometry has proven elusive. We explore the effect of canopy morphology on vegetated channels flow structure and resistance by treating the canopy as a porous medium characterized by an effective permeability, a property that describes the ease with which water can flow through the canopy layer. We employ a two-domain model for flow over and within the canopy, which couples the log-law in the free layer to the Darcy-Brinkman equation in the vegetated layer. We validate the model analytical solutions for the average velocity profile within and above the canopy, the volumetric discharge and the friction factor against data collected across a wide range of canopy morphologies encountered in riverine systems. Results indicate agreement between model predictions and data for both simple and complex plant morphologies. For low submergence canopies, we find a universal scaling law that relates friction factor with canopy permeability and a rescaled bulk Reynolds number. This provides a valuable tool to assess habitats sustainability associated with hydro-dynamical conditions.

Highlights

In the last decades, an increasing number of countries have introduced restoration practices to promote the sustainable management of rivers[1]
Computational fluid dynamics (CFD) models, which explicitly resolve the flow field around individual stems, have increased our understanding of how different types of vegetation affect flow resistance and have allowed to quantify the impact that species-specific morphology has on fluid flow and friction.[37]
The model treats the canopy layer as a porous medium and, as a result, has a number of advantages: (i) the canopy layer morphology is uniquely characterized by one macroscopic parameter, i.e., the canopy effective permeability, (ii) the model input parameters such as the height of the water level and the canopy can be directly estimated by remote sensing and acoustic techniques[30,46], and (iii) flow properties within and above the canopies are directly correlated to canopy morphology through its effective permeability and are quantified by closed-form expressions

Summary

Introduction

An increasing number of countries have introduced restoration practices to promote the sustainable management of rivers[1]. Computational fluid dynamics (CFD) models, which explicitly resolve the flow field around individual stems, have increased our understanding of how different types of vegetation affect flow resistance and have allowed to quantify the impact that species-specific morphology has on fluid flow and friction.[37]. Their upscaling from the stem- to the canopy-scale is not trivial due to the often prohibitive computational burden associated with modeling plant-plant interaction, such as the sheltering effect induced on one individual plant by the presence of others[37,41]. The mean velocity profile above and within the canopy layer is obtained by coupling the log-law u(z)

Methods

Results

Conclusion