Barbara Zanuttigh

Roll waves simulation using shallow water equations and Weighted Average Flux method

The weighted average flux method is used to represent trough 1-D shallow water equations the development of natural roll waves in rectangular channels. The method is reformulated in such a way that all source terms are incorporated into the local Riemann problem by means of a useful transformation of the equations, maintaining second-order accuracy of the solution. A code based on this method has been developed and results of numerical applications to a Venturi channel and to the attenuation of waves are presented to check for well known situations how accurately the source terms are evaluated. The code is applied to reproduce Brocks experiments on roll waves performed in a rectangular laboratory channel. The numerical solution accurately represents roll waves evolution due to uniform flow instability as well as wave intensity increase due to instability and wave coalescence. A sensitivity analysis of the numerical solution to changes of computational parameters is performed, in order to explain the discrepancies among computed and experimental values.

Experimental analysis of the impact of dry avalanches on structures and implication for debris flows

Objectives of this work are to experimentally analyse the dynamic impact of dry avalanches on structures and to examine the possibility of extending the results to debris flows; to identify structure efficiency in terms of extension and shape of the deposition area; to numerically validate the adequacy of shallow-water equations in reproducing the impact process and the maximum force on the obstacle; finally to propose an analytical expression for estimating the design force. Experiments were carried out on two dry sandy mixtures flowing down a steep chute and impacting on obstacles of different shape that reproduce check-dams, filter-dams, “houses” and flow-breakers. Effects of mixture composition, obstacle shape and orientation— with respect to mean flow direction—on force values and deposit extension were examined, showing that only check-dams can significantly reduce the kinetic energy and retain the flowing material. Numerical simulations were performed with a 1D code, based on shallow-water equations and the weighted average flux method, to represent forces on an infinite high obstacle (i.e., a wall) in time. Promising results allowed the use of a simple expression directly derived from momentum balance to compute the force exerted by the flow on the structure for given upstream flow depth and velocity. Limitations of the experiments in reproducing impact on defence works in real events are highlighted and suggestions for improving structural design are drawn.

Minimum channel length for roll-wave generation

The initial phase of roll-wave development is investigated by means of spatial linear stability analysis using the St. Venant equations, subject to a pointwise time-varying oscillating disturbance. The predicted spatial growth is compared with both Vedernikovs results and those computed with a fully non-linear model. It is shown that for large values of the channel slope Vedernikovs theory systematically overpredicts the roll waves spatial growth rate, whereas the present analysis yields significant improvements. A modification of Montuoris criterion for the minimum channel length prediction is finally proposed, which agrees with available experimental data independently of the channel slope.

Oblique Wave Transmission Over Low-Crested Structures

Wave transmission over low-crested structures have often been the subject for research, as the wave field behind these structures determines what will happen in this area. Detached low-crested structures are often parallel to the coastline and in most cases wave attack will be perpendicular to this coastline and therefore, perpendicular to the structure. This situation can be simulated by small scale physical modeling in a wave flume. Recent research, including all data of the above given references and new extensive data sets, has enlarged the insight on the topic. The results from 2D tests are: (1) prediction formulae for the wave transmission coefficient K; and (2) a description of change of spectral shape because of wave transmission. In some situations low-crested structures are not parallel to the coast. T-shaped groynes are an example, but also breakwaters for a harbor where under very extreme storm surge, the structure can be considered as low-crested. In these situations wave attack is very often not perpendicular to the alignment of the structure and in many situations even quite oblique wave attack and transmission occurs. But what will be the difference with perpendicular attack? More in detail: (1) are the prediction formulae for k still valid; (2) is the spectral change (more energy to high frequencies) similar to perpendicular wave attack; (3) is there any influence of short-crestedness of waves; and (4) are wave directions similar in front of the structure and after transmission? Only a three-dimensional investigation in a short-crested wave basin can give answers to these questions. Within the EU-project DELOS these tests have been performed and are the subject of the paper.

Influence of Relative Roughness and Reynolds Number on the Roll-Waves Spatial Evolution

The paper investigates the influence of the resistance coefficient variability onto the spatial development of roll-waves. Two models, based on time-asymptotic solutions of the linearized St. Venant equations, subject to either impulsive or oscillating perturbation, have been modified by including the dependence of the resistance coefficient on flow conditions, wall roughness, and fluid viscosity. Independently of the perturbation type, it has been shown that the hypothesis of constant resistance coefficient leads to underestimate the disturbance spatial growth. Theoretical predictions are finally compared with results of a fully nonlinear model and with literature experimental data for several combinations of Froude and Reynolds numbers and relative roughness values. The representation of variability of the resistance coefficient fundamentally improves the performance of minimum channel length criteria, whereas its neglect may lead to noncautious channel design.

Numerical modelling of debris surges based on shallow-water and homogeneous material approximations

Abstract The objective of this contribution is to analyse the formation of debris waves in natural channels. Numerical simulations are carried out with a ID code based on shallow-water equations and on the weighted averaged flux method. The numerical code represents the incised channel geometry with a power-law relation between local width and flow depth and accounts for all source terms in the momentum equation. The debris mixture is treated as a homogeneous fluid over a fixed bottom, whose rheological behaviour alternatively follows Herschel-BulkJey, Bingham or generalised visco-plastic models. The code is applied to real debris flow events that consisted of a single wave and multiple surges, in particular in the Illgraben catchment (Switzerland) and in the Cortina d’Ampezzo area (Dolomites). Numerical results are presented and compared with available flow depth registrations. A statistical analysis of debris waves shows that a good representation of wave statistics can be obtained with a proper calibra...

Analysis of Wave Reflection from Structures with Berms Through an Extensive Database and 2DV Numerical Modelling

This paper analyses wave reflection from permeable structures with a berm, including reshaping cases. Data are obtained from recent wave flume experiments and from 2DV numerical simulations performed with the COBRAS-UC code. The objectives of this research were to identify the proper representation of the average structure slope to be included in the breaker parameter and to check the performance of the formula for the reflection coefficient developed for straight slopes by the Authors. Based on the observation that for reflection, differently from what happens for overtopping and run-up, the whole slope below sea water level (SWL) is important, the slope to appear in the breaker parameter is evaluated as a weighted average of the structure slope below the berm level and the average slope in the run-up/run-down area. The inclusion of this slope in the proposed formula allows to extend its prediction capacity to structures with a berm and a fair agreement with both experiments and simulations is obtained.

EFFECT OF LAYOUT ON FLOATING BREAKWATER PERFORMANCE: RESULTS OF WAVE BASIN EXPERIMENTS

Aim of this contribution is to investigate the relevance of the layout on the performance of floating breakwater schemes under oblique waves. An experimental investigation was carried out in the wave basin of the Maritime Laboratory of Padua University, Italy. The facility dimensions are 3.8m x 20.6m x 0.8m. Several regular and irregular longcrested waves were generated and two different layouts (Iand J-shaped) and three obliquities (0°, 30°, 60°) were tested. With increasing wave obliquity, wave transmission decreases, mooring forces due to snapping decrease and link forces slightly increase. The J-shaped configuration determines basically the same effects with regards to both transmission and loads. The maxima of link forces are not much greater than the average loads and this is relevant for fatigue and reliability considerations.

Experimental analysis of the segregation of dry avalanches and implications for debris flows

The objectives of this contribution are to analyse and quantify the segregation process of dry granular avalanches, both parallel and perpendicular to the flow. Experiments were carried out using two dry granular mixtures, a steep chute of variable length and a collecting bin divided by transversal and longitudinal sectors, in which the flowing material falls down at the chute outlet. The free-falling of the flow in the segregator bin, the filling in time of the bin itself, the grain-size composition of the bin content with varying the distance from the chute outlet and axis are examined by image analysis and by sieving each bin cell. Segregation is very effective and rapid along flow direction whereas appears to be substantially negligible perpendicularly to the flow. The rapidity of flow segregation can be directly related to flow depth, whereas effects of mixture grain-size composition seems not appreciable. The longitudinal grain-size composition profile in time is reconstructed, showing coarser particles concentrated at the flow front and on the flow surface and fine fractions prevailing at the tail and at the bottom. Possible extension of these results to debris flows are discussed considering scale problems and comparing the results with other available experimental works and with field observations of natural events.

WAVE TRANSMISSION AT LOW-CRESTED STRUCTURES, INCLUDING OBLIQUE WAVE ATTACK

A part of the DELOS research focused on wave transformation at low-crested structure and is summarised in this paper. Several flume tests have been carried out within the project to analyse wave transmission on rubble mound structures and simultaneously an existing database has been extensively increased by receiving data from other researchers in the world. This new database consists of more than 2300 tests and has been used to come up with the best 2D wave transmission formula for rubble mound LCS. Oblique wave attack on LCS was a second objective within DELOS. Small scale model results were produced and analysed leading to new transmission formulae for smooth LCS and to conclusions on 3D effects for both rubble mound and smooth LCS.