Scaling and modelling of turbulent flow over a sparse canopy

TL;DR

This study uses direct numerical simulations to analyze turbulent flow over sparse canopies, proposing a new local stress-based scaling and models that better predict flow fluctuations by accounting for canopy effects.

Contribution

It introduces a height-dependent local stress scaling and develops models that improve turbulence prediction over sparse canopies compared to traditional methods.

Findings

Local stress-based scaling aligns fluctuations with smooth wall flows.

A mean-only drag model improves fluctuation estimates.

Homogenised models cannot capture local canopy effects.

Abstract

The turbulent flow within and above a sparse canopy is investigated using direct numerical simulations. The balance of Reynolds to viscous stresses within the canopy is observed to be similar to that over a smooth wall. From this, a scaling based on their local sum is proposed. Using the conventional scaling based on the total stress, the velocity fluctuations are typically reported to be reduced within the canopy compared to smooth walls. When the proposed height-dependent scaling is used, however, the fluctuations are closer to those over smooth walls. This suggests that, in a large part, the effect of the canopy can be reduced to the modification of the local scaling, rather than to the direct interaction of the canopy elements with the turbulence. Based on this, a model is proposed that consists of a drag that acts on the mean flow alone, aiming to produce the correct scaling without modifying the fluctuations directly. This model is shown to estimate the fluctuations within the canopy better than the conventional, homogeneous-drag model. Nevertheless, homogenised methods are not able to reproduce the local effects of the canopy elements. In order to capture these, another model is proposed that applies the mean-only drag on a truncated representation of the canopy geometry.