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Modelling Procedures
Published in Vanesa Magar, Sediment Transport and Morphodynamics Modelling for Coasts and Shallow Environments, 2020
Generally, the conservation equations for constituents are advection–diffusion equations, for salinity, temperature, and biochemical constituents, with first-order decay for oil spills, or other degrading constituents. Some models, such as Delft3D, have a formulation for cohesive and noncohesive sediments, making them ideal options for both open beach and estuarine environments. Bed evolution is modelled with the Exner equation, which includes bedload transport processes through computation of the sediment transport rate. The seabed evolves at a slower rate than the hydrodynamic forcings. This means that the bed does not need to be updated at every hydrodynamic timestep. A morphodynamic updating factor, or MORFAC parameter, defines the number of skipped hydrodynamic timesteps between morphological updates. The model predictions need to be tested with different MORFAC parameter values to make sure that the results are still reliable with MORFAC larger than 1.
Sediment Control in Rivers and Reservoirs
Published in Larry W. Mays, Optimal Control of Hydrosystems, 1997
where Ei,t is the bed elevation at station i and at time t measured from a designated reference datum, di,t is the depth of flow at station i during time t, αt is the energy distribution coefficient associated with station i at time t, hi,t is the energy loss from station i + 1 to station i during time t, Vi,t is the flow velocity at station i during time t, and g is the gravitational constant. The sediment continuity (routing) equation (Exner equation) is expressed as
Upstream channel degradation triggered by a meander cutoff: Potential replacement for channel dredging
Published in Wim Uijttewaal, Mário J. Franca, Daniel Valero, Victor Chavarrias, Clàudia Ylla Arbós, Ralph Schielen, Alessandra Crosato, River Flow 2020, 2020
K. Naito, L. Guerrero, H. Valverde, Y. Estrada, F. Fuentes, B. Santillan, G. Valvidia, J.D. Abad, T. Iwasaki
The temporal evolution of the river profile is described by the Exner equation as follows: 1−λp∂η∂t=−∂qT∂x
Extended Engelund–Hansen type sediment transport relation for mixtures based on the sand-silt-bed Lower Yellow River, China
Published in Journal of Hydraulic Research, 2019
Kensuke Naito, Hongbo Ma, Jeffrey A. Nittrouer, Yuanfeng Zhang, Baosheng Wu, Yuanjian Wang, Xudong Fu, Gary Parker
Wright and Parker (2004) and He et al. (2012) use an entrainment-based formulation for the Exner equation of sediment continuity. That is, they calculate the variation in bed elevation and surface GSD in terms of the difference between an entrainment rate into suspension and a deposition rate from suspension. Here, however, we use a flux-based formulation, in which the local sediment transport rate equals the capacity value for the flow, and the bed elevation variation is related to the downstream gradient in streamwise sediment transport rate. The use of the flux form is likely generally appropriate because the LYR dataset was developed under quasi-equilibrium conditions, in which the flow carries bed material at its transport capacity and sediment deposition to the bed and sediment entrainment of the sediment from the bed are locally in balance (Long & Zhang, 2002; Zhang et al., 1998).
A coupled two-dimensional numerical model for rapidly varying flow, sediment transport and bed morphology By Xin Liu, Julio Ángel Infante Sedano and Abdolmajid Mohammadian
Published in Journal of Hydraulic Research, 2018
If the Authors only consider suspended load transport, then the bed update equation (i.e. the Authors’ Eq. (5)) should be refined as: If only bed load transport is considered (as indicated by test cases applied by the Authors) and the capacity assumption is applied (though not as justified as a non-capacity model), the Authors’ Eq. (4) for suspended load transport is not needed while the original Exner equation without the entrainment and deposition fluxes (i.e. Eq. (D5)) can be used along with a formula for bed load transport rate: Further, if bed load transport is non-capacity based, which is physically more justified and applicable (Cao et al., 2016), a non-capacity transport equation for bed load along with the corresponding bed update equation should be used, which can be found in many models (e.g. Cao et al., 2016; Furbish et al., 2012; Pelosi & Parker, 2014; Qian et al., 2015, 2017; Wu, 2004, 2007).
1D morphodynamic modelling using a simplified grain size description
Published in Journal of Hydraulic Research, 2018
Benoît Camenen, Claire Béraud, Jérôme Le Coz, André Paquier
The RubarBE code is a 1D hydraulic mobile-bed numerical code, which solves the Barré de Saint-Venant equations (shallow water equations). These equations are solved using a second-order Godunov-type explicit and upwind scheme, which is shock capturing and robust enough to describe transitions between subcritical and supercritical flows (El kadi Abderrezzak et al., 2008; El kadi Abderrezzak & Paquier, 2009). It should be noted that hydraulic parameters are resolved with a cell-centred scheme (computed in the middle of two cross-sections), while sediment parameters (sediment transport and bed evolution) are resolved with a node-centred scheme (computed at each cross-section) (El kadi Abderrezzak et al., 2008). This particular feature of the RubarBE numerical scheme improves its stability especially when bed evolves dramatically. Sediment variables are computed at each time step as well as the riverbed geometry, which is updated using the Exner equation for the sediment continuity: where φ is the porosity, is the cross-sectional area of the bed above a reference datum, is the volumetric sediment transport, t is the time, and x is the longitudinal direction.