Recent analysis of equilibrium and quasi-equilibrium channel geometry in engineered (fixed-width) rivers has successfully shown that two temporal scales can be distinguished, with quasi-static (long-term) and dynamic (short-term) components. This distinction is based on the fact that channel slope cannot keep pace with short-term fluctuations of the controls. Here we exploit the distinction between the two temporal scales to model the transient (so time-dependent) phase of channel response, which is the phase wherein the channel approaches its new equilibrium. We show that: (a) besides channel slope, also the bed surface texture cannot keep pace with short-term fluctuations of the controls, and (b) mean transient channel response is determined by the probability distributions of the controls (e.g., flow duration curve rather than flow rate sequence). These findings allow us to set up a rapid numerical method that determines the mean transient channel response under stochastic controls. The method is based on distinguishing modes (i.e., sets of controls) and takes the probability density of each mode into account. At each time step, we compute the mode-specific flow, sediment transport rate, and corresponding change in bed level and surface texture. The net change within the time step is computed by weighting the mode-specific changes in bed level and surface texture with the probability density of each mode. The resulting mean transient channel response is a deterministic one, despite the controls being stochastic variables. We show that the proposed method provides a rapid alternative to Monte Carlo analysis regarding the mean time-dependent channel response.

@en

An engineered alluvial river (i.e., a fixed-width channel) has constrained planform but is free to adjust channel slope and bed surface texture. These features are subject to controls: the hydrograph, sediment flux, and downstream base level. If the controls are sustained (or change slowly relative to the timescale of channel response), the channel ultimately achieves an equilibrium (or quasi-equilibrium) state. For brevity, we use the term “quasi-equilibrium” as a shorthand for both states. This quasi-equilibrium state is characterized by quasi-static and dynamic components, which define the characteristic timescale at which the dynamics of bed level average out. Although analytical models of quasi-equilibrium channel geometry in quasi-normal flow segments exist, rapid methods for determining the quasi-equilibrium geometry in backwater-dominated segments are still lacking. We show that, irrespective of its dynamics, the bed slope of a backwater or quasi-normal flow segment can be approximated as quasi-static (i.e., the static slope approximation). This approximation enables us to derive a rapid numerical space-marching solution of the quasi-static component for quasi-equilibrium channel geometry in both backwater and quasi-normal flow segments. A space-marching method means that the solution is found by stepping through space without the necessity of computing the transient phase. An additional numerical time stepping model describes the dynamic component of the quasi-equilibrium channel geometry. Tests of the two models against a backwater-Exner model confirm their validity. Our analysis validates previous studies in showing that the flow duration curve determines the quasi-static equilibrium profile, whereas the flow rate sequence governs the dynamic fluctuations.

@en

The active layer model (Hirano, 1971) is frequently used for modeling mixed-size sediment river morphodynamic processes. It assumes that all the dynamics of the bed surface are captured by a homogeneous top layer that interacts with the flow. Although successful in reproducing a wide range of phenomena, it has two problems: (1) It may become mathematically ill-posed, which causes the model to lose its predictive capabilities, and (2) it does not capture dispersion of tracer sediment. We extend the active layer model by accounting for conservation of the sediment in transport and obtain a new model that overcomes the two problems. We analytically assess the model properties and discover an instability mechanism associated with the formation of waves under conditions in which the active layer model is ill-posed. Numerical simulations using the new model show that it is capable of reproducing two laboratory experiments conducted under conditions in which the active layer model is ill-posed. The new model captures the formation of waves and mixing due to an increase in active layer thickness. Simulations of tracer dispersion show that the model reproduces reasonably well a laboratory experiment under conditions in which the effect of temporary burial of sediment due to bedforms is negligible. Simulations of a field experiment illustrate that the model does not capture the effect of temporary burial of sediment by bedforms.

@en

Potential consequences of climate change are the amplification of extreme discharge events and an overall increase in fl ow rates. Their effects on river future morphodynamic behaviour (e.g., 100 years) has been assessed through numerical simulation of different climate scenarios@en

Reliable hazard analysis is a crucial step in flood risk management, and for large river systems, the effects of breaches on downstream regions should be taken into account. Accounting for these breaches in hazard analyses is often termed ‘hydrodynamic system behaviour’ analyses, and has become increasingly popular in flood risk assessment. Methods to perform such analyses usually focus on high water levels as a trigger for dike breaching. However, the duration of high water levels is known to be an important criterion in the mechanisms that cause dike breaching, for example piping. This study aims to demonstrate the effect of the duration on hydraulic system behaviour analyses, using a computational framework in which two dike breach triggering methods are compared in a large river system. The Dutch Rhine is used as a case-study. The first method triggers dike breaches based on water levels, and the second method is dependent on both waterlevel and duration, with the relationship of the two variables inferred via expert opinion. This comparison is made for dike failure probabilities based on the proposed future standards of protection.@en

When rivers are forced by statistically invariant boundary conditions (i.e. an upstream water discharge, upstream sediment discharge and downstream base level that fluctuate around constant mean values), and are not subject to any forcing with a temporal trend (e.g. no uplift/subsidence, no sea-level rise), they tend to a morphodynamic equilibrium state over time. Due to continuously changing boundary conditions a river may never reach its mean equilibrium state, yet it will tend to it continuously, and if the boundary conditions change at a sufficiently slow pace, the river may be in a quasiequilibrium state. Therefore, studying the equilibrium state of a river may help us to better understand the long-term trends that are observed in natural rivers, such as for instance the ongoing bed degradation in the Dutch Rhine. Available models used to predict the morphodynamic equilibrium state are mainly analytical ones that start from the assumption that there is always normal flow, during all stages of an imposed upstream hydrograph (Prins, 1969; Blom et al., in preparation). This means the hydrograph may include variable flow rates due to for instance flood waves, yet the hydrodynamic state of the river is modelled as a sequence of consecutive normal flow regimes. Variable flow rates, tidal forcing and spatial variations in, for instance, river width, however, can induce backwater effects, also in the equilibrium state. Here we propose an efficient model that describes the river’s behaviour also outside of the normal flow zone, in the so-called backwater segment (e.g. Nittrouer et al. 2012). The efficiency of this model results from the approach to solve for the equilibrium in a space-marching solution procedure (i.e. a backwater alike solution procedure), rather than using a time-marching model where long simulation times (e.g. 1000 years) are required before an equilibrium situation is reached. @en

A river that is forced by statistically invariant boundary conditions and is notsubject to any forcing with a temporal trend continuously tends to anequilibrium state in which the bed level and texture fluctuate around stable meanvalues. Studying the equilibrium state of a river can therefore help us explainsome of the long-term trends that are observed in natural rivers (de Vriend,2015). A sufficiently accurate solution of the 1D morphodynamic equilibrium statecan be found by running a Saint- Venant-Exner/Hirano model until the long-termaverage morphodynamic state has converged to a stable value. Yet, this oftenrequires hours to days of computation time and it is therefore not suitable fora quick assessment of the morphodynamic equilibrium state. In this research we studythis state using a newly developed numerical spacemarching model (i.e. abackwater-alike solution procedure) that allows us to compute a river’sequilibrium profile in backwater dominated reaches efficiently. @en

In this paper, a cell-colony based formalism for the healing of superficial wounds is presented. The paper incorporates the migration, proliferation, and death of constituent cells, in the context of wound healing. The present study considers wound healing under ischemic conditions where a bacterial infection develops, which impairs the motility of the constituent cells. In this work, the performance of the immune response system is incorporated in the sense that migrating leukocyte are modelled which engulf the infectious pathogens. The model is based on both deterministic and stochastic principles. Simulation results are discussed in a biological context.@en