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This report focusses on discontinuous behaviour of hydraulics and morphology in rivers. The varying widths, slopes and bed levels that can be observed in mountain rivers can induce rapid, or discontinuous changes at a short lengthscale. When present, these discontinuities have a major impact on changes in water and bed levels during floods. In this study, existing theories on discontinuous solutions are applied to river flows with mobile beds. The propagation rate and stability of a discontinuity are analysed with the Lax shock-wave criterion. Effects of transitions in flow regime are described qualitatively by solving the Rankine-Hugoniot relations. Attention is paid to the effect of river bed mobility on discontinuous flows.

In this report the analytical and numerical formulations, testing and calibration of the third generation wave hindcast model WAVEWATCH are presented. WAVEWATCH is specially designed to operate in a combined wave-current model. The main attention is focussed on numerical aspects of the model, including academic test cases and comparison with other third generation wave models (which do not include current effects). Furthermore, preliminary results of calculations for a south westerly storm in the southern North Sea are presented to illustrate the effects of wave-current interactions in the southern North Sea in such conditions

A bed-load sediment transport formula has ben devlopd for every fraction of the sediment mixture. All existing bed-load formula have been reanalysed on their application for this purpose (Kalinske, Einstein, Meyer-Peter and Muller) as well as adaptations by different other authors

A simple mathematical model for the simulation of river meandering processes is presented and analysed. The model is schematized as follows: computation of steady-state flow field and riverbed topography; and computation of bank erosion rate as a function of the near-bank hydraulic and morphological properties. The model is linear for the prediction of flow field and river bed topography, while geometrical non-linearities arise from the bank erosion equation. The flow and river bed model is derived by fully coupling flow field, bed topography and sediment transport and it (roughly) accounts for the secondary flow momentum convection.

A number of qualitative properties of a first-order gradient transport model for turbulent density-stratified flow is analyzed. The dynamical stability of a statically stable shear flow is considered to re-examine certain arguments found in the literature which are in favour of the possibility of instability. Real flows seem to be stable in the sense that in homogeneous turbulence sharp interfaces do not arise spontaneously. Furthermore the development of an interface between two homogeneous layers is dealt with, and is found to be in line with the stability analysis and with experimental evidence reported in the literature.

This report deals with second order, two-dimensional low frequency waves induced by the non-linear interactions of the first order component waves in a two-dimensional short wave field. The convolution to calculate the averaged two-dimensional low frequency wave spectrum is developed. Any given two-dimensional short wave spectrum can be used as an input of this convolution. The theoretical results are compared with field data measured in the North Sea. The observed low-frequency wave energy is considerably in excess of the predicted value which may be due to low-frequency waves not correlated with the local wind waves.

The existing relationships based on Durand's method to predict pressure gradients for slurry flow in pipelines appear to be inadequate when accounting for a wide range of variables such as particle size and relative density as well as concentration. Using the coal, sand and iron ore data collected from various literature sources with the aid of non-dimensional analysis, new equations for the case of the heterogeneous flow regime were derived on the base of nondimensional parameters. The equations have the same structure for each material considered, but the coefficients are different.

The wave motion on-and-in Berm breakwaters as well as the reshaping process have been studied. Measurements were carried out to study wave interaction with a reshaped Berm breakwater. These tests were used for verification of a numerical model capable of simulating both the wave motion on as well as inside the structure. This numerical model has been extended. The wave model has been combined with a new morphological model for cross-structure transport. This extended model is capable of simulating the reshaping process of Berm breakwaters and gravel beaches.

OpenEarthTools contains, apart from a lot of other tools in various programming languages, the probabilistic reliability methods FORM and Monte Carlo. This document aims at describing and providing background information and examples on the FORM and Monte Carlo implementation available in OpenEarthTools.

A spectral evolution model is implemented of the extended Boussinesq equation which can be used for varying bathymetry even in deep water region. In this model, a contribution of the triad nonlinear interaction can be segregated from that of the bottom shoaling effect. For a simple onedimensional case, an attempt to express the triad interaction as a source function term in the energy balance equation is shown. Numerical sensitivities for different initial phases and different frequency band widths are investigated. It is observed that the numerical results are dependent on the initial phases. An ensemble mean of many realizations or a frequency averaged estimation of a single realization with a very fine frequency resolution provides convergent results. These numerical estimations of the spectral model agree well with experimental data for finite-amplitude waves propagating over a bar in shallow water.

This report evaluates the B009 data of the back-ward facing step experiment which was one of a series of the experiments that were designed and conducted by Hofland and Booij (2004) and De Ruijter (2004). In this experiment, the flow field and the pressure field were measured (by PIV and pressure sensors) during the displacement of a single stone from a granular bed. This measurement shows similarities to the results from previous experiments. At the time the stone started to move, two flow structures were found to be responsible for the entrainment: a large-scale sweep (u'>0 and v'>0), causing increased quasi-steady forces, and an embedded small-scale structure with vertical velocity fluctuations, sigma(v'), causing turbulence wall pressure fluctuation (TWP). In the four entrainments, these structures were present simultaneously in the instantaneous flow fields.

In this report, transport problems are solved with a particle method that takes into account the Eulerian background flow field. Dispersion and other transport problems can be solved applying this model, as long as the corresponding transport process is formulated with a flux gradient relation, i.e., the advection-diffusion equation. The particle method has been made consistent with such a transport process. Since many 3D flow models are formulated in general coordinates, the 3D particle displacements are also given with respect to such a coordinate system. Analytical and numerical aspects of this particle method have been studied. The effectiveness of the method has been demonstrated with two academic test cases including streamlines in a recirculation zone and grid dependency in a discharge problem.

A derivation is presented of a general cross-section averaged model of longitudinal dispersion, which is based on the notion of the advection of tracer particles. Particle displacement length and particle travel time are conceived as stochastic variables, and a joint probability density function is introduced to arrive at an integral advection model for the cross-section averaged concentration. Starting from this model special advection models known from the literature are obtained in a consistent way. These models, in which only the travel time is a stochastic variable, predict skewed tracer concentration contributions of the kind observed in the field, but satisfy the condition of approach to Gaussian behaviour for large spreading times. A relationship between the particle displacement length and the longitudinal dispersion coefficient is derived. The application of advection models to non-uniform rivers and the relationship with the dead-zone model are outlined.

A survey of literature is made on reservoir sedimentation, one of the most threatening processes for world-wide reservoir performance. The sedimentation processes, their impacts, and their controlling factors are assessed from a hydraulic engineering point of view with special emphasis on mathematical modelling. The objective of this study is to find the remaining gaps in the understanding of the relevant features, and the needs for further research. The physics of sediment distribution (such as delta formation and density currents) and the present modelling techniques are identified for various types of reservoirs. Attention is also paid to the operational aspects and the environmental impacts of the reservoir on the river-system morphology. Finally the methods to reduce the sediment inflow, to reduce the accumulation, or to remove the deposits are described. Evaluating the state of knowledge it is clear that a large number of physical processes are involved which are not well understood or hard to simulate. Recommended is to develop more comprehensive mathematical models and to do more specific laboratory research.

A two-layer mathematical model is presented for sedimentation in reservoirs where turbidity currents are to be expected. As the model is two-dimensional in plan, the suspended-sediment concentration of the turbulent underflow is described by a depth-integrated form of the convection-diffusion equation originally proposed by Galappatti in 1983. The bed-level variations governing this model are described by a depth-integrated sediment balance. For closure of the model various closure relations are required based on the vertical distribution of flow and sediment of the turbidity current. A semi-empirical model, presented to describe these distributions, is used to quantify boundary shear stresses, suspended-sediment transport rate, and the adaptation scales in Galappatti's equation. Additionally a discussion is given on the applicability of various existing relations for interfacial mixing, as well as on relations for the near-bed sediment concentration. The presented model, and the proposed simplified models deduced from it, can be used for various types of reservoirs and to more conventional computations such as for saline underflows.

General design aspects of settling tube systems for fall velocity analysis of sand are reviewed, with emphasize being placed on detection methods for particle arrival at the lower end of the settling column and the various sources of errors. This is followed by a detailed discussion on the development of an improved settling tube system employing an underwater balance. In order to achieve a high degree of accuracy, stability and damping, the weighing system includes a feedback mechanism which consists of a solenoid-magnet unit and a differentiator; this yields a resolution of 10 micro newton. The overall accuracy of fall velocity is better than 3% (which takes into consideration concentration effect) and the precision is better than 4% (at a confidence level of 95%). Data acquisition and processing are performed by means of a microcomputer with a l2-bit AID converter, sampling in the velocity domain.

Derivations and analyses of basic equations for I-dimensional sediment-laden flow (concentrations up to about 10% of volume) on a mobile bed are presented . Equations of mass and momentum conservation have been derived by means of a control section as well as by depth integration. Therefore a three-layer approach has been used (i.e., bed layer, bed-load layer, and suspended-load layer). Despite the assumptions of uniform sediment, fixed banks and constant width the derivations can easily be extended for more general models. Analysis of the basic equations b means of the method of characteristics showed that with increasing concentration wave celerities alter, and showed that critical flow occurs at Froude numbers less than unity. A stability analysis of the equations showed that the criterion for occurrence of roll waves in supercritical flow is also modified by the increased concentration. Due to increased concentrations roll waves can occur in sediment-laden flow at lower Froude numbers than in clear water flow.

This report is the result of a project, called "comparative tests on commercial and newly designed waterrams", carried out by the Delft University of Technology and the Foundation of Dutch Volunteers in Rwanda. The aim of this project was twofold: - to test new, and cheap (i.e. locally constructable and maintainable) types of hydraulic rams, - to compare several commercial types, in order to make a "consumers guide" for developing countries. At the Laboratory of Fluid Mechanics of the Delft University of Technology the most essential aspects of the behaviour of commercially available rams were compared. Valve behaviour, delivery head, delivered quantity and efficiency were accentuated. Samples of the rams, tested in the laboratory were checked in Rwanda on reliability, durability and possibilities for local maintenance.