Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 3818591, 12 pages

http://dx.doi.org/10.1155/2016/3818591

## Interactions Study of Hydrodynamic-Morphology-Vegetation for Dam-Break Flows

^{1}School of Ocean Science and Environment, Dalian Ocean University, Dalian, Liaoning 116023, China^{2}State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, Sichuan 610065, China^{3}State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning 116025, China^{4}Yuanyanggou National Ocean Park, Panjin, Liaoning 124010, China

Received 26 July 2016; Revised 26 September 2016; Accepted 16 October 2016

Academic Editor: Angelo Di Egidio

Copyright © 2016 Mingliang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study models a dam-break flow over a bed by using a depth-averaged numerical model based on finite-volume method and computes the dam-break flow and bed morphology characteristics. The generalized shallow water equations considering the sediment transport and bed change on dam-break flow are adopted in the numerical model, and the vegetation effects on the flow and morphological changes are considered. The model is verified against three cases from the laboratory and field data documented in the literature. The numerical results are consistent with the measured results, which show that the model could accurately simulate the evolution of the dam-break flows and the morphology evolution of bed within a computational domain with complex plant distribution. The results show that the riparian vegetation in the waterway narrows the channel and reduces the conveyance capacity of river. The flood flow is diverted away from the vegetation community toward two sides and forms a weak flow region behind the vegetation domain. The resistance of plants markedly reduces the flow velocity, which directly alters the fluvial processes and influences the waterway morphology.

#### 1. Introduction

Increase in catastrophic flood events has attracted increasing attention on the prediction of their dynamics and bed change evolution, especially in relation to riverine plant effect. Usually, grasses, shrubs, and mangroves, growing in watercourses and floodplains, are key members of the water ecosystem. They play important roles in water purification, flood control, and maintenance of bank stability, but they also create nonpositive obstruction effect on flood propagation in waterways. Recently, interactions between flow, morphology, and aquatic plant have been studied in the laboratory and field-scale experiments. Manners et al. (2014) believed that rapid expansion of tamarisk led to a narrower channel, which pushed the Yampa River into a new equilibrium having altered fluvial processes [1]. Some researchers employed flume experiments to investigate the potential effects of living vegetation and large wood on river morphology, specifically aiming to explore how different wood input and vegetation scenarios impact channel patterns and dynamics [2]. Asami et al. (2012) investigated the morphological characteristics of refugium where riverine plants survived large floods [3]. Because numerical method has its advantages of wide application range, repeatability, and low cost compared to other methods, some effective and efficient numerical methods were developed for understanding flood wave propagation in urban areas, complex open channels, and overland flow systems [4]. Dam-break flows were usually formed in mixed flow regimes with discontinuities; the numerical schemes that were often used for such studies include the shock-capture schemes, such as Total Variation Diminishing schemes (TVD) and Godunov type schemes [5–8]. During a flooding hazard involving rapid transients, interaction between dam-break waves and topography changes could be significant; however, the interaction was ignored in the early numerical models for simulating dam-break flows over mobile beds.

During dam-break flow conditions, the flow velocity is large, the sediment concentration is high, and the bed varies so rapidly that their effects on the flow cannot be ignored [9]. To correctly predict the consequences of a dam failure in a complex topography, the interaction between flow and bed morphology must be modeled using a coupled solution [9–12]. However, such models are based on either fixed rectangular grids or uniform curvilinear boundary-fitted grids and, therefore, simulate the large-scale flow features on a structured grid system, which may consequently reduce the modeling accuracy and efficiency [13–15]. One of the major objectives of studies was to investigate the turbulence structure in vegetated environments [16, 17]. However, there are restrictions and limitations about the knowledge of the positive or nonpositive effects on the topography change caused by vegetation. The crucial contributions of plants to the flood hydrodynamics and the bed change need to be recognized.

In the present study, a depth-averaged hydrodynamic and sediment transport model, based on finite-volume method, is developed to simulate the flood waves and bed change due to vegetation effect. For improving simulation accuracy, local mesh at selected locations is refined by using triangular mesh. The proposed model is first used to calculate the dam-break flows over fixed bed and to compare the water levels and velocities with measured data. Then, the bed changes of dam-break flood are computed to investigate the temporal and spatial variability in the bed elevation. Finally, the hydrodynamic variation and the evolution of bed elevation through the rigid vegetation domain are investigated and discussed.

#### 2. Mathematical Equations

##### 2.1. Governing Equations

The depth-averaged shallow water equations were obtained by integrating the Navier–Stokes equations over the flow depth, consisting of continuity equation and momentum equations for depth-averaged free surface flows. The conservative and vector forms of the 2D shallow water equations are written in (1) and (2), respectively, as follows:where is the time, and are Cartesian coordinates describing the horizontal plane, , , and are vectors of the conserved flow variables and the convection fluxes in the and directions, respectively, and is source term [18].where is the flow depth; and are the depth-averaged velocity in the and directions, respectively, and and are the bed shear stress term with and components defined by the velocities and , respectively. , , and is Manning’s coefficient. Here, is the water level, is the gravitational acceleration, and is density of the water and sediment mixture in the water column, determined by . Here, is the volumetric concentration of total-load sediment dimensionless, is density of the water and sediment mixture in the bed surface layer, determined by , is the porosity of the bed material, and and are water and sediment densities. and are the sediment entrainment and deposition fluxes, respectively. and are the vegetation drag forces in the and directions.

The sediment deposition and entrainment are estimated as follows:where is an empirical coefficient and is the settling velocity of sediment particle [9] given as follows:where is kinematic viscosity and is the sediment diameter. in (4) is the depth-averaged sediment transport capacity given as follows:where is the bed-load sediment transport capacity given as follows:In (7), is the modified parameter, is the Shields parameter such that , is the threshold Shields parameter, and .

The bed deformation can be determined as follows:where is the bed surface elevation above a reference datum.

##### 2.2. Vegetation Resistance

The vegetation effect on the flow was included to the momentum equations as an internal source of resistant force per unit fluid mass. Therefore, the drag force exerted on vegetation per unit volume can be expressed as follows [16]:where is the drag force coefficient, is the vegetation density defined as number of vegetation elements per square meter, is diameter of a vegetation element, and is the height of vegetation.

Equation (9) is derived from experimental and field data and it has been extensively used in wave propagation and it could be also employed to describe dam-break wave propagation.

#### 3. Numerical Method

##### 3.1. Finite-Volume Method

A standard finite-volume method with Roe Riemann solver for wet and dry computation has been developed. The discretization of the governing equations was based on the finite-volume method, for which the unstructured triangular mesh is shown in Figure 1. The conserved variables were defined at the cell centers and represented the average value over each cell. Hence, the integral form of (1) over the th control volume can be written as follows:where subscript indicates the element number and subscript indicates the side of the element. is the advective fluxes term of the water and is the diffusive fluxes term of the water. is the control volume of the th element. Using Green’s theorem, (10) becomeswhere is the average value of the conserved variables over the th cell and is stored at the center of each cell, with . is the boundary of and is the area of the th cell. is the outward surface normal vector of , with , where is the included angle between the outward normal vector and the direction.