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

Tatyana Dyakonova,Alexander Khoperskov

doi:10.1088/1742-6596/973/1/012032

Tatyana Dyakonova, Alexander Khoperskov

Open Access

https://doi.org/10.1088/1742-6596/973/1/012032

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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 nM 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 nM on the amplitude and spatial scale of perturbation of the bottom relief.

Highlights

The models of shallow water are successfully applied for calculation of a wide range of geophysical currents including the dynamics of surface and groundwater, landslides [1], torrential flows [2, 3], the pyroplastic and granular masses movement [4], the simulation of large-scale atmospheric, sea and ocean currents [5], and the technospheric security problems [6, 7]
The numerical simulation of hydrodynamic currents of surface water on a realistic terrain relief usually containing a wide range of scales of bottom inhomogenieties has shown that these inhomogeneities exert an additional resistance to the flow
This factor should be taken into account when choosing the value of the Manning coefficient nM

Summary

Introduction

The models of shallow water are successfully applied for calculation of a wide range of geophysical currents including the dynamics of surface and groundwater, landslides [1], torrential flows [2, 3], the pyroplastic and granular masses movement [4], the simulation of large-scale atmospheric, sea and ocean currents [5], and the technospheric security problems [6, 7]. To simulate the dynamics of channel and floodplain currents in the shallow water models, it is essential accounting for the hydraulic resistance [8, 9, 10, 11, 12]. The latter can be described using a number of developed phenomenological models [12]. The Manning roughness coefficient is a composite value generally taking into account the influence of vegetation, various obstacles, meandering, turbulence and other factors [13, 14, 15, 16]. The coefficient nM is assumed to be a function of coordinates and may depend on the water layer thickness, H, under the conditions of the nonstationary flow [20]

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