Sediment transport in open channel flow has a great impact on siltation of rivers, reservoirs and artificial channels, and it is therefore one of the major topics studied in the hydraulic realm. In spite of the intensive investigation done in the past, the transport mechanism of sediment particles in open channel flow is still not fully understood owing to the chaotic behavior of turbulence, complex interaction between solid and flow phases, effect of sediment grain size distribution and so on. According to the transport mechanism, the processes of sediment transport can be roughly classified into two categories, bed load transport and suspended sediment transport. There are different standards can be used to divide two kinds of transport, in general, bed load transport usually includes unneglectable turbulence modulation (caused by the form drag of sediment particles) and heavily interacts between sediment particles and channel boundary. On the contrary, suspended sediment transport is dominated by the flow properties, i.e. movements of sediment particles follow closely to the flow motion. This study focuses on the suspended sediment transport under dilute situation in open channel flow in which the influence of sediment particles on flow and interaction between particles play minor roles in the overall process.
In the conventional analysis, suspended sediment transport is regarded as an advection-diffusion process, called turbulent diffusion, which is driven mainly by turbulence. In steady state, distribution of sediment particles along with a vertical section can be seen as the result of equilibrium between particle downward intention caused by
gravity and the spread of particles which is disturbed by turbulence. If the location of sediment particles can be described in terms of sediment concentration and present turbulent eddy viscosity as the degree of turbulence disturbance, the celebrated Rouse profile can be derived. As such, a fairly well estimation of long term average sediment concentration can be obtained. On the other hand, as the governing equation of suspended sediment transport in unsteady flow, the advection-diffusion equation is widely applied for the simulation of morphology development, assessment of reservoir lifespan and so on.
Nevertheless, when it comes to conducting a more delicate analysis of suspended sediment transport, a deterministic estimation is no longer satisfactory. To get advanced information, researchers introduce the probabilistic concept to the analysis of suspended sediment transport. One of them linked the Langevin equation with the advection-diffusion equation through Fokker-Plank equation and developed the stochastic particle tracking model (a detailed derivation will be provided in §2.). The model illustrates the probabilistic trajectory of sediment particles in each realization and provides a bridge from the behavior of individual sediment particles to diffusion phenomena of sediment concentration. It shows the assumptions implied in the advection-diffusion equation, a so-called Fickian assumption and memoryless property. Apart from the Fickian assumption that describes the behavior of particle spreading, memorylessness is another important assumption about the transition of system between different states. In short, it
is referred to as the statement that future status of system is only dependent on its current status.
However, studies of wall-bounded turbulence, the turbulence in boundary layer, pipe, and open channel flow, indicate the existence of coherent structures which have their own
“order” to form, develop, and dissipate. This “order” implies the appearance of temporal and spatial correlations among flow properties (Nezu & Nakagawa 1993). The anisotropy and inhomogeneity of turbulence coherent structures make the traditional Gaussian random walk incompatible with the path that sediment particles actually take (Adrian &
Marusic 2012). Thus, it is desirable to refine the model based on the random walk theory to provide more realistic simulation of suspended sediment transport and meanwhile to keep its conciseness without involving moment or force balance equations.
1.1 Problem statement
As mentioned previously, the Rouse profile yields results that are consistent with experimental and field data in long term average and the advection-diffusion equation is applied to various engineering implementations. However, even in the steady state, sediment concentrations will fluctuate because large turbulence eddies, or the so-called turbulence coherent structures disturb sediment particles (Cellino & Lemmin 2004).
It shows that the diffusion based models only fit the bulk/long-term-average phenomena of the turbulent diffusion, and some behaviors of suspended sediment
transport are missing. All the factors that influence the spreading of the sediment particles are lumped in one important parameter, i.e., the sediment diffusion coefficient. The non-clearance of the mechanism works behind the coefficient makes it hard to be determined without the aid of fitting or regressing with the data when the predicted sediment concentration of the diffusion based model deviates from the reality.
Despite turbulence motions are chaotic, the motions have a local trend and correlation in time and space owing to the existence of large eddies. Statistical properties of the turbulence structures may give information of suspended sediment particle movement in the flow field. Once the movement of suspended sediment particles can be illustrated, the physical meaning of the sediment diffusion coefficient can be revealed. In addition, the correlations between sediment flux and the turbulence coherent structure have been reported in experiments (Noguchi & Nezu 2009; Salim et al. 2017). Turbulence coherent structures should be more comprehensively considered in the sediment transport model if at all available.
The aim of this study is to better investigate the role of the sediment diffusion coefficient on suspended sediment particle movement in open channel flow. Meanwhile, a novel stochastic process that incorporates the memory effect to represent the turbulence flow structure will be introduced. An improved random walk model based on this process is suggested.
1.2 Research hypotheses
The turbulence structures contribute to the local trend of the flow and sediment particle movements. Whether the effect of the local trend will remain in the long term phenomena is another story. For example, in the near wall region of wall bounded turbulence, the turbulence coherent structures of the ejection and sweep events are associated with sediment entrainments and affect the instantaneous local sediment concentration (Dwivedi et al. 2011; Rashidi et al. 1990;); notwithstanding, such events are highly intermittent and sporadic. The conventional analysis based on the advection-diffusion process can give a fairly well estimation of long term average concentrations.
The importance of these events in the explanation of the relationship between the bulk diffusion phenomena and single sediment particle movements in sediment transport is questioned.
Moreover, when the turbulence coherent structure disturbs the sediment particles, particles seem to be carried by the flow at longer time scales, which differ from the Kolmogorov time scale that is used in the simulation of the particle tracking model. Is it merely the property of coherent structure that is not worth mentioning in the overall transport mechanism? Or it has a profound physical meaning for flow to carry particles in suspension? With respect to the entrainment of particles from the river bed, the intensity of flow events is not the only factor that determines whether a particle is picked up. The temporal scale of the flow events is also important (Dwivedi et al. 2011). The situation may be similar for particle moving in flow fields.
Thus, the two hypotheses that are considered in this study are as follows.
1. The ejection and sweep events in the near wall region affect long-term average sediment concentrations.
2. The temporal scale of the flow events is essential to understanding the relationship between the turbulent diffusion and turbulence intensity.
Both of the hypotheses are related to the descriptions of sediment particle movement in the turbulence diffusion. After verifying the two hypotheses, the necessity of introducing a novel framework of the stochastic particle tracking model for suspended sediment transport that can represent the existence of the flow structures in open channel flow will been shown.
1.3 Overview of the thesis
The background knowledge and the connections of this study with existing work will be mentioned in §2. After that, two sections follow, modeling suspended sediment transport under the influence of turbulent ejection and sweep events and incorporating the particle memory effect under the impact of turbulence structures into suspended sediment transport modeling. Two sections are contained in §3 and 4 respectively. At the end, the overall conclusions will be provided in §5.
At the first section of the thesis, the temporal scale of large flow events is incorporated into the stochastic particle tracking model. As the first attempt to consider
the random walk based model of sediment transport with turbulence coherent structures, this study focuses on the ejection and sweep events which are related to the hairpin vortex in the near wall region. The results of simulation demonstrate that the temporal scale of flow structures plays an important role in carrying sediment particles in suspension.
In the second section, the mathematical impact of including temporal scale of turbulence coherent structures in the random walk based model is discussed in terms of memory effect. A novel stochastic process is proposed to analyze the relationship between the statistical properties of turbulence velocity and the spreading behavior of the fluid particles. Based on the process, the framework of a new random walk model for suspended sediment transport is suggested.