Flume experimental evaluation of the effect of rill flow path tortuosity on rill roughness based on the Manning–Strickler equation

doi:10.1016/j.catena.2014.01.011

CATENA

Volume 118, July 2014, Pages 226-233

https://doi.org/10.1016/j.catena.2014.01.011 Get rights and content

Highlights

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Different rill morphologies self-generated in a flume.
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Rill hydraulics and rill morphologies were observed.
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Rill roughness was highly variable and relates to rill morphology.
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Flow path tortuosity can be used to assess local friction effects.

Abstract

Numerous soil erosion models compute concentrated flow hydraulics based on the Manning–Strickler equation (v = k_St R^2/3 I^1/2) even though the range of the application on rill flow is unclear. Unconfined rill morphologies generate local friction effects and consequently spatially variable rill roughness which is in conflict with the assumptions of (sectional) uniform channel flow and constant channel roughness of the Manning–Strickler equation.

The objective of this study is to evaluate the effect of rill morphology on roughness and hence to assess the Manning–Strickler roughness coefficient (k_St) by rill morphological data. A laboratory experiment was set up to analyse rill hydraulics and roughness of I.) Free Developed Rill (FDR) flows and II.) Straight Constrained Rill (SCR) flows in the flume. The flume experiment generated Manning–Strickler roughness coefficients (k_St) between 22 m^1/3 s^− 1 and 44 m^1/3 s^− 1 reflecting a potential area of the roughness parameter uncertainty. It was found that FDR experiments generated significantly lower k_St values compared to SCR experiments, because skin and local friction effects in the FDR experiments were more efficient reducing flow velocity probably due to higher energy dissipation. Rill flow path tortuosity (Tort) was used to describe the rill morphology of the experiments and correlation statistics between Tort and k_St identified considerable explanatory capacity of rill flow path tortuosity on rill roughness. The flume study demonstrated that a regression model between Tort and k_St can be used to assess local friction effects of unconfined rill morphologies and hence to reduce the area of uncertainty of the Manning–Strickler roughness parameter.

Introduction

Concentrated flow in numerous soil erosion models is computed based on uniform flow equations designed for river scale hydraulics (Govers et al., 2007) and therefore the application on rill flow is limited. Uniform flow equations represent turbulent and uniform open channel flow (Chow, 1959) and unconfined rill flow in nature deviates from this concept. Unconfined rill morphologies generate local friction effects and consequently spatially variable rill roughness which is conflict with the assumptions of the commonly used flow equation of Darcy–Weisbach, Manning or Chezy (Gilley et al., 1990).

However, practicable input data requirements enable straightforward modelling and therefore particularly the Manning–Strickler equation is often used in physical based erosion models (Govers et al., 2007) even though consequential gaps have been intensively discussed in the past (e.g., Gilley et al., 1990, Govers et al., 2007, Julien and Simons, 1985, Moore and Burch, 1986, Nearing et al., 1997). Channel friction is scale dependent as there is a changeover from skin friction to form drag due to pressure differences around individual obstacles in a channel (Judd and Peterson, 1969, Lee and Ferguson, 2002) and therefore the constant Manning–Strickler roughness coefficient is insufficient to describe variable friction effects. Non-uniform flows of step and pool morphologies can generate considerable supplementary friction loss due to transient flow conditions and hydraulic jumps which can dominate total flow resistance (Comiti and Lenzi, 2006, Comiti et al., 2007, Curran and Wohl, 2003, MacFarlane and Wohl, 2003). Turbulent and rough channel flow conditions, required by the Manning–Strickler equation (Julien and Simons, 1985) might be achieved in large scale rill flows, but the assumptions of approximate steady-state and uniform channel flow might fail for rill as well as river scale flows.

Moreover, Manning's equation lacks the ability to describe the flow of an actively eroding rill because of variable interactions between rill flow, soil erosion and sediment transport (Nearing et al., 1997). The sediment transport of a rill differs over time and space as an unsaturated rill flow needs to recover within a distance and based on this, sediment concentration controls the rill erosion rate (Liu et al., 2007, Wirtz et al., 2012) and consequently the rill morphological development. This conflicts with the often used model assumption that rill flow occurs on a surface with a fixed rill structure during the entire erosion process (Parsons et al., 1997). Various researchers suggested relations between sediment transport and flow hydraulics to be implemented in physical based soil erosion models to account for the effects of transient runoff processes (e.g. Aksoy and Kavvas, 2005, Lei et al., 1998, Nearing et al., 1997, Smith et al., 2011, Takken et al., 2005). For example Lei et al. (1998) presented a finite element model which self-generates the incision of a rill over space and time, even though lateral rill morphological impacts on the rill flow were neglected in this model.

However, Merritt et al. (2003) argued that most erosion models are inappropriate for predicting catchment scale and event-based sediment transport because of the lack of readily available watershed data and/or unsuitability of the model assumptions and therefore simplified flow equations are still in demand. Manning's equation is commonly accepted for overland flow as well as stream flow models and therefore it is preferable to use one equation for various model applications (Hessel et al., 2003). However, there is a gap between the complex rill flow in nature and idealized channel flow concepts commonly used to simulate such processes in watershed scale, even though the magnitude of the gap might vary. The objective of this study is to evaluate this gap and to explore interactions between rill morphology and rill roughness based on experimental data. A flume study was designed to develop unconstrained meandering rill erosion but also straight in line rill erosion morphologies to I.) explore a potential range of Manning–Strickler roughness due to different rill morphologies and II.) to evaluate the effect of rill flow path tortuosity on rill roughness.

Section snippets

Experimental design

The experiment was carried out in a 1.95 m long, 0.60 m wide and 0.35 m deep flume with a 10% inclination (Fig. 1). At the inlet a water reservoir with a 0.35 m wide rectangular opening was installed to provide a steady state inflow over the crest of the reservoir. At the bottom of the flume a system of drainage outlets was installed to set the soil subsurface to free drainage condition. The interface between the soil and the drainage outlets was an 8 cm thick gravel layer that provided even

Flume experimental observations

Free Developed Rill (FDR) experiment: When the adjusted inflow entered the prepared soil bed of the flume a shallow ca. 1 to 3 mm deep uniform sheet flow generated (Fig. 3A). The average sheet flow velocity was ca. 20 to 30 cm s^− 1. Various preferential flow paths developed because of the scattered soil aggregates on the surface and/or because of sheet flow erosion of less resistant particles during simulated rainfall treatment and/or sheet flow. When the front of the sheet flow entered the

Discussion

When the thalweg of a channel deviates from a straight channel alignment, the flow deviates from uniform flow condition as well. This circumstance has been ignored in numerous soil erosion models since uniform flow equations are preferentially used to calculate rill flow regardless the apparent limits of application. The present flume study was carried out to evaluate supplementary friction effects of a non-uniform flow based on the Manning–Strickler concept and to explore the potential of rill

Conclusions

This study demonstrates the impact of rill morphology on the Manning–Strickler rill roughness coefficient (k_St) based on free developed rill (FDR) and straight constrained rill (SCR) experiments. Two different discharges and two different initial flume conditions (FDR and SCR) were used to develop various rill morphologies and based on this, various rill flow conditions were generated in the flume. The experiment illustrates a wide range of Manning–Strickler roughness coefficients (from 22 m^1/3 s⁻

Acknowledgements

This research was kindly supported by the USDA ARS National Soil Erosion Research Laboratory, West Lafayette, USA, scientific staff and technicians. We also thank the Austrian Marshall Plan Foundation for the financial support.

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Citation Excerpt :
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Flume experimental evaluation of the effect of rill flow path tortuosity on rill roughness based on the Manning–Strickler equation

Highlights

Abstract

Introduction

Section snippets

Experimental design

Flume experimental observations

Discussion

Conclusions

Acknowledgements

Catena

Geomorphology

Geomorphology

J. Hydrol.

Geomorphology

Earth Sci. Rev.

Catena

Catena

Geomorphology

Environ. Model. Softw.

Soil Technol.

Geomorphology

J. Hydrol.

Catena

Catena

Open-Channel Hydraulics

Dimensions of standing waves at steps in mountain rivers

Water Resour. Res.

A programmable rainfall simulator for field plots