# Numerical analysis of an averaged model of turbulent transport near a roughness layer

## DOI:

https://doi.org/10.21914/anziamj.v53i0.5071## Keywords:

Centre manifolds, Turbulent boundary layer, roughness## Abstract

We formulate and numerically analyse the averaged model of dispersion in turbulent canopy flows. The averaging is carried out across the flow, for example over the river depth. To perform the averaging, we use the general approach suggested by Roberts and co-authors in the late 1980s, which is based on centre manifold theory. We derive an evolution partial differential equation for the depth averaged concentration, involving first, second and higher order derivatives with respect to the downstream coordinate. The coefficients of the equation are expressed in terms of parameters characterising the turbulent flow. Preliminary numerical results are demonstrated. In particular, it is shown that the advection and diffusion coefficients coincide with their values obtained earlier for the flow over a smooth bottom in the limit of large depths.**References**

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## Published

2012-05-25

## Issue

## Section

Proceedings Engineering Mathematics and Applications Conference