Bottom friction models for shallow water equations: Manning's roughness coefficient and small-scale bottom heterogeneity

TL;DR

This paper investigates how small-scale bottom heterogeneity influences the Manning roughness coefficient in shallow water models, using simulations to relate bottom perturbations to flow resistance.

Contribution

It introduces a method to relate bottom heterogeneity parameters to the Manning coefficient through computational simulations.

Findings

Manning coefficient depends on bottom perturbation amplitude and scale

Flow velocity profiles are affected by bottom heterogeneity

Simulation results enable better parameterization of bottom friction

Abstract

The correct description of the surface water dynamics in the model of shallow water requires accounting for friction. To simulate a channel flow in the Chezy model the constant Manning roughness coefficient is frequently used. The Manning coefficient n M is an integral parameter which accounts for a large number of physical factors determining the flow braking. We used computational simulations in a shallow water model to determine the relationship between the Manning coefficient and the parameters of small-scale perturbations of a bottom in a long channel. Comparing the transverse water velocity profiles in the channel obtained in the models with a perturbed bottom without bottom friction and with bottom friction on a smooth bottom, we constructed the dependence of n M on the amplitude and spatial scale of perturbation of the bottom relief.