Two-Dimensional Two-Phase Depth-Integrated Model for Transients over Mobile Bed

Abstract

Fast geomorphic transients may involve complex scenarios of sediment transport, occurring near the bottom as bed load (i.e., saltating, sliding, and rolling) or as suspended load in the upper portion of the flow. The two sediment transport modalities may even coexist or alternate each other during the same event, especially when the shear stress varies considerably. Modeling these processes is therefore a challenging task, for which the usual representation of the flow as a mixture may result in being unsatisfactory. In the present paper, a new two-phase depth-averaged model is presented that accounts for variable sediment concentration in both bed and suspended loads. Distinct phase velocities are considered for bed load, whereas the slip velocity between the two phases is neglected in the suspended load. It is shown that the resulting two-phase model is hyperbolic, and the analytical expression of the eigenvalues is provided. The entrainment/deposition of sediment between the bottom and the bed load layer is based on a modified van Rijn transport parameter, whereas for the suspended sediment a first-order exchange law is considered. A numerical finite-volume method is used for the simulation of three dam break experiments found in the literature, which are effectively reproduced in terms of both free surface elevation and bottom deformation, confirming the key role played by the solid concentration variability even for two-phase models

Exploring a semimechanistic episodic Langevin model for bed load transport: Emergence of normal and anomalous advection and diffusion regimes

“…The nature of bed load transport is highly stochastic and complex, even under steady state conditions, involving a wide range of spatiotemporal scales, from grain-scale kinematics to bed form-scale migration [Sekine and Parker, 1992;Papanicolaou et al, 1999;Ancey et al, 2006;Ancey, 2010;Hill et al, 2010;Singh et al, 2009Singh et al, , 2011Singh et al, , 2012Ramesh et al, 2011;Furbish et al, 2012a;McElroy and Mohrig, 2012;Julien and Bounvilay 2013;Guala et al, 2014;Keylock et al, 2014;Cristo et al, 2015]. This inherent stochasticity is mostly a result of the particle-fluid interactions and particle-particle interactions, leading to diffusion (also referred to as dispersion) of particles during their movement [Martin et al, 2012].…”

Approximate Solutions for Ideal Dam‐Break Sediment‐Laden Flows on Uniform Slopes

“…In fact, as pointed out by Cao et al (2017), the SHSM equations have been extended to model coastal processes (Kim, 2015;Xiao et al, 2010;Zhu & Dodd, 2015), watershed erosion processes (Kim et al, 2013), subaqueous sediment-laden flows and turbidity currents (Hu & Cao, 2009;Hu et al, 2012), and sharply stratified processes (Li et al, 2013;Spinewine & Capart, 2013;Zech et al, 2015). Most recently, shallow water twophase models have been developed to better resolve fluvial processes (Cristo et al, 2015;Li et al, 2017) and debris flows (Li et al, 2018a(Li et al, , 2018b). Pivotal to the success of SHSM models are the recent advances in both computer technology and numerical methods.…”

Numerical Simulation of a Dam-Break Wave Propagating Over an Erodible Floodplain in Presence of a Structure

“…A brief description of the model presented in [17] is provided below, whereas the reader is referred to the original reference for further details about model assumptions and limitations, as well as for the method employed for the numerical simulation. Since, in the present application the suspended load has been neglected, the model consists of equations expressing the mass and momentum conservation for the liquid (Eqs.…”

“…where c is the threshold shear stress for sediment motion and B is the magnitude of Mohr-Coulomb stress at the bottom, with s the static friction coefficient. Even if the coefficient  and CD could be estimated from existing empirical formulas, their expression has been deduced based on the analysis of uniform flow conditions [17], obtaining the following relations:…”

“…In the present paper, a numerical study of the propagation of a dam-break wave over an erodible floodplain in presence of a rigid obstacle is carried out. To this aim, the shallow-water two-phase model by [17] is used for reproducing the same geometry of the fixed-bed test case by [6].…”