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Transmission of long wave through permeable breakwater
This study aimed at providing information about the behaviour of a long wave encountering a permeable breakwater of the rubble mound type. To avoid the practical difficulties mentioned above, a measuring system has been developed, which makes use of the theory of transfer functions. Model tests were carried out in a flume with a computer controlled wave generator, which was programmed to absorb the reflections reaching the wave board. The reflection and transmission characteristics of a series of breakwater models were obtained, including phase changes in the reflected and transmitted waves. The influence of a number of important parameters (stone diameter, porosity, structure width) on the transmission was investigated. The tests were performed with regular waves only. After the model experiments were completed, a series of filtration tests was carried out in order to measure the permeability of the granular materials used in the models.
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Numerical Modelling of Infragravity Wave Response during Delilah
In this paper the nonlinear numerical model SHORECIRC is applied to simulate the intragravity wave conditions on two days during the 1990 Delilah campaign. In order to simulate the wave conditions an algorithm has been derived which synthesizes a directional of/shore wavefield from data including the bound, directional low-frequency components. The model-data comparison shows that the mean short wave transformation on the real bathymetry is predicted correctly, and that the mean longshore current is predicted very well for one of the two days without tuning the parameters. Furthermore, the structure of the infragravity spectrum as measured in the nearshore array is correctly represented but the energy level is under'estimated.
Research report for Rijkswaterstaat, RIKZ.
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On the generation of surfable ship waves in a circular pool: Part I: physical background & wave pool design
| Master thesis |
Civil Engineering and Geosciences
2007-06-29
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| Author: |
De Schipper, M.A.
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Mentor:
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Stelling, G.S. · Stive, M.J.F. · De Koning Gans, H.J., ir · Reniers, A.J.H.M. · Uijttewaal, W.S.J. · Henriquez, M. · Labeur, R.J. · Van Thiel de Vries, J.S.M.
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| Keywords: |
waves · surfing · ship · pool
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Surfing as a sport is growing. Locations with good surfing conditions are limited and therefore crowded. The growing interest for the sport led to a new concept, surf pools. Surf pools mimic good surfing conditions found along the coast.
This thesis is about the technical feasibility of a new surf pool concept, creating surfing waves in a circular pool by towing ship-like hulls around. The hulls are towed along the outer wall of the pool and waves generated by these hulls propagate inwards and break on an island in the middle of the pool. The waves break around the island which theoretically leads to endless surf rides.
The initial design as suggested by Webber is based on a pool diameter of 200 m and a water depth of 3 m. The objective of his design to generate 2 m high waves for intermediate to expert surfers.
Because of the lack of knowledge about ship induced waves in such an enclosed environment, a physical and a numerical model study are carried out.
Various hull sizes are towed in a towing tank and the surface elevations are measured and analyzed. From this physical model study it was concluded that the wave pattern behind a hull is the result of a complex interference pattern and is easily disturbed when the velocity beside the hull becomes large. The difficulties of wave generation by a hull therefore lie in the return currents. The magnitude of the return flow is a function of the blockage, the percentage of the cross section of the pool blocked by the hull. In case the blocking and the velocity are too large, water accumulates in front of the hull and the wave field behind the hull is disturbed, the so-called trans-critical regime. Maximum wave height is found when to towing a hull at the onset of this trans-critical regime.
The initial wave pool design is evaluated, and it was concluded that the water depth of 3 m is insufficient to generate the desired 2 m waves. Therefore an amended design is presented. Water depth is increased to 7 m and the generation area is enlarged to reduce the blockage to 5%. The large generation area causes a weak return flow and therefore less turbulence in the pool. In such a cross section it is considered technically possible to generate 2 m high surfable waves.
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Wave transmission at low-crested structures
This report contains an analysis of data on wave transmission. It is restricted to wave transmission at low-crested permeable breakwaters. All data used are from tests with irregular waves. These data were earlier gatherd in Delft Hydraulics' report: "Data on wave transmission due to overtopping by J.W. van der Meer ((1990).
Aim of the research: Until now wave transmission is described by various formulas in which terms appear which contain more than one parameter. This makes it hard to recognize the influence of an individual parameter. The aim of the analysis presented in this report is to look at all parameters involved in a separate way and to come up with a formula which can predict wave transmission at low-crested breakwaters. This formula should be practically usable and reasonable reliable.
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| 5 |
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Boussinesq modelling of wave-induced particle velocities
In this thesis, the modelling of the horizontal velocity field under waves using Boussinesqtype models is studied. Special attention is paid to the prediction of bottom velocities in view of sediment-transport formulations. Boussinesq-type models describe the propagation of weakly non-linear shallow-water waves. The depth-dependence of the velocity field has been removed in deriving the equations, which are therefore stated in the surface elevation and one single horizontal velocity variable, the so-called computational velocity. After integration of the Boussinesq-type equations, the horizontal velocity field must be reproduced in some kind of postprocessing. Many different forms of Boussinesq-type equations exist. They differ in frequency-dispersion and shoaling characteristics as well as in the used computational velocity variable. Various different forms ofBoussinesq-type equations are compared in view of their capability in reproducing the horizontal velocity field. A set of equations with good frequency-dispersion and shoaling behaviour and stated in terms of the depth-averaged horizontal velocity is selected for numerical treatment. The method to reconstruct the horizontal velocity field from the depth-averaged velocity is described. The selected equations are implemented in an existing time domain Boussinesq model (Beji and Battjes, 1994) supplemented with a formulation to obtain the horizontal velocity field. The model is validated against surface elevation data from three different wave flume experiments (see Dingemans, 1994a and Luth et al., 1994). The time domain model is used to predict the horizontal velocity field, especially bottom velocities, obtained from wave flume experiments of non-breaking regular waves propagating over a submerged bar (Luth et al., 1994). The results show encouraging agreement with the measurements. The comparison is limited inshore by the wave breaking process. In order to predict horizontal velocities in breaking waves, a spectral Boussinesq model in which a spectral breaking term is incorporated (Eldeberky and Battjes, 1995), is used. This model is based on the assumption of uni-directional wave propagation and therefore only yields surface elevations. The spectral model is extended to compute the depth-averaged horizontal velocity and, subsequently, the complete horizontal velocity field. The extended spectral model is verified against wave flume experiments of irregular (partially) breaking waves propagating over a nearly monotonic sandy beach (Arcilla et aI., 1994 and Roelvink and Reniers, 1995). In the comparison of computations with measurements, the focus is on bottom velocity time series and resulting third odd velocity moments. Good results are obtained for long waves. For shorter waves a significant underestimation of the crest values and velocity moments is found. It is concluded that the accuracy in predicting horizontal velocities with Boussinesq models is comparable to the accuracy in predicting surface elevations. The latter is limited by the inaccurate frequency dispersion of Boussinesq models in deeper water.
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| 6 |
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Wave Physics in a Tidal Inlet - Part I: On the time scales of wave processes. Part II: Depth-induced breaking: a comparison on the performance of three models
Part I: On the time scales of wave processes.
To systematically improve the SWAN model a study on the wave physics in a tidal inlet was carried out. The third-generation SWAN model was used to compute the wave processes in a tidal inlet for storm conditions. The computed wave processes are propagation (shoaling, refraction and frequency shifting), generation (wind input), non-linear wave-wave interactions (quadruplet wave-wave interactions and triad wave-wave interactions), dissipation (white capping, depth induced breaking and bottom friction), and the work done by the currents against the radiation stresses. The results were normalised, which resulted in the time scales of all wave processes. The time scales were of the order 100s – 1,000s, except for the work done by the currents against the radiation stresses, which is of the order of 1,000s – 10,000s.
Part II: Depth-induced breaking: A comparison of the performance of three models.
Depth-induced breaking is a subject that has been widely studied, resulting in many scalings on the Battjes and Janssen model. The Battjes and Janssen model, the biphase scaling and the Nelson scaling were selected to compare results in terms of significant wave height. The parameter of interest is the model coefficient . The models were tested with the SWAN model on three different test cases; two reef cases and one sloping bottom profile. The wave period appeared to have a strong influence on the prediction of the significant wave height, in particular on the biphase scaling. The best model over the three test cases statistically is the Nelson scaling.
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The kinematics of broadbanded waves
Ocean waves are random and their crests evolve non-linearly. Yet commonly used wave models correctly incorporate only one of these aspects: the models either use non-linear regular wave theory whilst ignoring the randomness or use linear random theory with empirical corrections close to the free surface. For the more realistic design and re-assessment of off-shore structures, it is important to have an accurate model of the flow within large waves. In this report a numerical wave tank is used to study the water-wave problem. The numerical wave tank has been developed by Taylor and Vijfvinkel [16] and incorporates the non-linearity and the irregularity of waves. Wave-wave interactions have been simulated numerically for the full hydrodynamic equations using the scheme developed by Craig and Sulem [1]. This is based on Fourier expansion for both the free surface and the velocity potential.
One advantage of this scheme is that it is possible to start with a linear group at the focus point, run the code backwards linearly in time and then restart the code running forward in time until the wave group focuses. After the restart, all the hydrodynamic non-linearities are included within the calculation. Typically, the non-linear focus point is shifted compared to the linear focus point and the peak surface displacement is higher than the linear value.
In this report the focusing and dispersion of fully non-linear wave groups on different water depths is studied. A procedure for linearising the focused surface profile is introduced. This allows us to study the effects of wave non-linearity on the phase speed of individual Fourier components within the wave group. The wave properties on the surface given by the numerical wave tank are used to calculate the internal kinematics. From these profiles non-linear Morison drag forces can be calculated and compared with drag forces estimated using a empirical modification to linear wave theory known as Delta stretching [6]. For uni-directional waves, we propose a simple variant on Delta stretching which produces global force predictions much closer to the fully non-linear solutions.
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An Experimental Study of Wave Forces on Slope
The phenomenon that waves break in sea has long been existing, but the nature of wave breaking and the effects it would bring have not been weIl understood. However, as nowadays more and more offshore installations go to deep sea and/or are operated under more violent wave climates, the effects, which are caused by breaking wave impingement up on the structures, are arousing the interest of people.
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A comparison of mathematical models for wave propagation in harbours
A wave entering a harbor will be diffracted and reflected, depending on the shape and the construction of
breakwaters, quays and other objects in the harbor. The incoming wave can increase or decrease in height and a resonance can occur. This affects the manouvering of ships and the movement of moored ships, which influences the loading and unloading of cargo. When planning a harbor or an extension of one, harbor authorities will be interested in the wave conditions in the harbor.
The phenomena of wave propagation in a constant-depth harbor can be described with diffraction theory. When the depth in the harbour varies, the wave propagation can be described by a combination of refraction and diffraction theory.
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The breaking of windwaves in deep water : Part I. Probalistic aspects : Part II. Observed breaking wave statistics
Part I Probabilistic aspects. An overview is given of literature on the statistics of breaking waves in open ocean. New approximations of the fraction of breaking waves and the distribution of breaking wave heights are presented and compared with results found in literature.
Part II Observed breaking wave statistics. This part is dedicated to the results of the field observations.
In this experiment visual observations of breaking waves passing a waverider buoy are carried out. The statistics of breaking waves are investigated from wave records of this buoy in which visually observed breaking waves are labelled.
Part III ontbreekt.
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Waves of long and short period
Research on waves, with focus on translation waves due to gate operations.
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| 12 |
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Electromagnetic waves
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Generation of low-frequency waves due to obliquely incident grouped short waves
Looking at a surfzone, one immediately notices the short breaking waves. Looking more carefully, will show in most cases that the wave height of the breaking waves is not constant, but varies in time.
Often one may observe that groups of relatively high waves are followed by groups of lower waves. This short wave groupiness may cause low frequency fluctuations in the nearshore zone by generating so called long waves. These are less noticeable, because of their longer time scale.
This study was made to see whether it is possible to predict the generation of long waves in the nearshore zone due to the groupiness of obliquely incident short waves, and if so, extend an existing numerical model, SURFBEÀT [Roelvink, 1991] to the case of obliquely incident waves.
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| 14 |
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Shallow foreshore wave height statistics
Wave height distributions on shallow foreshores deviate from those in deep water due to the effects of the restricted depth-to-height ratio and of wave breaking. Laboratory data of wave heights on shallow foreshores of different slopes have been analysed to determine these effects and to derive generalised empirical parameterisation. A model distribution is proposed consisting of a Rayleigh distribution or a Weibull distribution with exponent equal to 2, for the lower heights and a Weibull with a higher exponent for the higher wave heights. The parameters of this distribution have been estimated form the data and expressed in terms of local wave energy, depth and bottom slope, yielding a predictive model that is to be significantly more accurate that existing expressions.
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| 15 |
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On the generation of surfable ship waves, Part II: the application of stereo photo technique measuring water surface elevation and surface flow velocities
Wave pools are designed to mimic surfing conditions as they exist along coasts. The Liquid Time Wave Pool concept, invented by Greg Webber, suggests a new method for wave generation. Waves are generated by a hull which moves in a channel. These "ship waves" break on a slope creating surf. Key feature of the concept is to make ship waves surfable. To investigate the possibility of creating surfable ship waves an experiment is conducted. During this experiment hulls are towed through a channel and the generated waves are measured using a stereo photo technique.
The objectives of this study are to:
1) Investigate the possibility of making ship waves surfable;
2) Investigate the capability of the stereo photo technique to measure water surface elevation and surface velocity over a specific area.
Existing theory offers the possibility to estimate wave fields using Froude depth numbers and the blocking of the channel cross section by the hull. The Froude depth number represents the ratio of the ship speed and the shallow water celerity.
When Froude depth numbers and blocking values are low, hull speeds are much smaller than the shallow water celerity. The regime is called sub-critical and a dominating secondary wave field is expected.
When Froude depth numbers and blocking values are high, hull speeds are high and currents around the hull can become critical. The hull speed when return currents become critical is called the limit speed. Hull speeds exceeding the limit speed account for the trans-critical regime. The trans-critical regime holds a dominating primary wave system and a negligible secondary wave system.
The angle of the generated wave determines the peel angle of the surfing wave. The peel angle is the angle enclosed by the wave crest and the path of the breakpoint. Peel angles mainly determine the surfer speed.
To gain insight in wave angles and surface velocities of ship waves and to verify existing ship wave theory a physical experiment is conducted. In the experiment hulls with different blocking coefficients are towed through a channel at different speeds covering the sub-critical and trans-critical regime. The wave field generated by the hull is simultaneously photographed by two distinct calibrated cameras. These stereo photos taken by the cameras are input to the stereo photo algorithm. The output of the algorithm is the water surface elevation and the surface flow velocity of the wave field.
It is found that the stereo photo technique offers a great possibility to derive water surface elevations and surface flow velocities. Water surface elevations are verified using parallel measurements by wave gauges. Accuracy of the technique highly depends on camera calibration which must be improved. Limiting factors for accuracy using the technique are the pixel resolution of the images, computational power and the density of the floats.
Using the stereo photo technique theory is validated. It is found that the wave field in the trans-critical regime holds strong currents. These strong currents make the trans-critical regime not suitable for surfing. The sub-critical regime holds weak currents and wave angles suit the range of the required peel angles.
The Liquid Time Wave Pool design should account for towing speeds and blocking coefficients leading to the sub-critical regime.
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Het gedrag van zakkingsfilters onder invloed van golfbelasting
Filterconstructies hebben als doel erosie te voorkomen in bepaalde delen van waterbouwkundige kunstwerken. Ze zijn opgebouwd uit een basislaag en een of meer filterlagen. Er zijn verschillende soorten filterconstructies. Ze worden over het algemeen zo gemaakt dat er geen erosie zal optreden van basismateriaal. Het is echter efficienter om een filter te ontwerpen op de erosie, die tijdens de levensduur ervan toelaatbaar wordt geacht; deze is uiteraard altijd groter dan nul. Een filter dat een
begrensde hoeveelheid erosie toelaat, heet een zakkingsfilter. Ondanks dat er veel winst te behalen vah met de toepassing van zakkingsfilters, worden ze nog maar zelden toegepast. Dit komt omdat er nog maar weinig bekend is over het complexe gedrag ervan. Vooral over de situatie bij goltbelasting bestaat veel tekort aan kennis. Dit onderzoek heeft als doel de kennis over zakkingsfilters onder
invloed van golfbelasting te vergroten.
Om vast te stellen bij welke golfbelasting er voor het eerst erosie ontstaat, is experimenteel onderzoek verricht in een stroomgoot. In de goot is een zakkingsfilter aangelegd. Hierover zijn gedurende een bepaalde tijd golven gestuurd om vervolgens de mate van erosie van het basismateriaal te bepalen. Elke golfhoogte veroorzaakt een bepaald erosievolume. Iteratief is gezocht naar de golfhoogte met een erosievolume van nul. De kritieke golfhoogte kan uiteindelijk worden bepaald door extrapolatie van een aantal erosievolumes naar nul. De kritieke golfbelasting Iijkt voonamelijk afbankelijk te zjjn van de mate waarin de orbitaalsnelheden gedempt worden door de filterlaag. De golfbelasting bij het begin van bewegen is hoger bij een kleinere nominale diameter van het filtermateriaal. Een dikke filterlaag betekent een hogere kritieke golfbelasting dan een dunne filterlaag. Verder is er een duidelijke periode-afhankelijkheid waar te nemen: hoe groter de golfperiode, hoe kleiner de kritieke golfuoogte. Uit vergelijkbare experimenten zander filter blijkt dat het basismateriaal zander filter minder snel gaat bewegen dan onder een uit te grote stenen opgebouwd filter. In het laatste geval is het nadeel van de extra opgewekte turbulenties rond de stenen grater dan het voordeel van de snelheidsdemping.
Als er transport van basismateriaal plaatsvindt bij golven hoger dan de kritieke golven, is het altijd gunstig om een zakkingsfilter te gebruiken. Tijdens het transport zijn er botsingen van het basismateriaal met de filterstenen. Dit veroorzaakt energieverlies waardoor het transport wordt afgeremd. Hoe dikker de filterlaag is, hoe groter het remmende effect zal zijn. Fijne filterstenen zorgen voar een betere remming dan grove filterstenen. Uit theoretische berekeningen van de snelheden in filterlagen komt naar voren, dat er geen duidelijk verband is tussen deze snelheden en het begin van beweging. Dit roll kunnen duiden op een belangrijke rol van turbulente snelheidsfluctuaties. In mortgelijke proeven bij een stationaire stroming werd de rol van deze turbulente snelheidsfluctuaties aangetoond. In andere proeven zonder een vrij wateroppervlak
werd een hogere kritieke golfhoogte gevonden. Ook dit zou verklaard kunnen worden door het verschil in turbulentie. Nauwkeurige snelheidsmetingen in de porien van filterlagen kunnen in een volgend onderzoek enige duidelijkheid scheppen over de lnvloed van turbulentie.
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Wave impact on horizontal platforms
This project is about wave impact on horizontal platforms. It investigates the interaction between
ocean waves, mainly during hurricanes, and harbour jetties in coastal areas. Various types of loads
can be identified when waves hit these kinds of coastal structures. The focus in this report will be on
vertical loads (upward and downward) on platform decks. This subject has only had little coverage in
studies on hydraulics or wave mechanics so far. The studies that are available differ SUbstantially in
everything from their origin and their goal, to their points of interest and their methods used. All this
makes that, before adding a new study to this list, it is very important to thoroughly review the
available literature to see which theories have been tested, which references have been looked at,
what methods have been used and what results were obtained.
Chapter 1 starts with the introduction to the project, describing the problem under investigation, the
goal to be achieved and the approach followed to do this.
Chapter 2 contains a literature review. This review summarises the work done on the SUbject from
around 1970 to today by various researchers and groups of researchers. The first thing that strikes in
this review is the non-uniformity and the lack of a clear framework that characterises most projects, at
least, as far as the presentation of the respective projects in research papers is concerned.
Researchers often follow their own trail, failing to comment on findings by others. Issues that are of
considerable importance to the exact understanding of the phenomenon are sometimes not
commented on or are solved without proper reasoning. These issues and the way this report deals
with them are listed in the end of this chapter.
The literature review does not end in a complete understanding on how wave loads should be
calculated. It shows a list of theories, analytical attempts and model tests trying to solve the problem,
in lots of different ways for lots of different reasons. In chapter 3 the current state of knowledge is
summarised. The wave impact process is separated into three components: Fpeak, the initial peak
force, F+, the slowly-varying positive load and F-, the negative load. For each of these components,
the parameters that influence their shape and magnitude are listed. After this, an overview will be
given on how well the various studies found in the literature deal with the issues mentioned above.
This will then result in a ranking which reflects the usability of their results. These results will then be
quantified for a couple of wave conditions, to see how the models compare.
Chapter 4 will describe model tests performed in the labs of HR Wallingford near Oxford. These tests
have not been commissioned or designed especially for this project, but many interesting findings
have been obtained from it nevertheless.
The next chapter, chapter 5, shows the way a model predicting the three impact force components
could look like. In important notion here is that the bounds of the validity of this model are defined by
the characteristics of the scale model it is derived from. The chapter ends with some guidelines for
designing a harbour jetty.
The last chapter, chapter 6, contains the conclusions and recommendations this project suggests.
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A comparison of overtopping behaviour over a permeable and impermeable crest: An insight into overtopping discharges and intensities
The purpose of this report is to investigate the differences in overtopping characteristics over the crest of a rubble mound breakwater when the crest is made either impermeable or permeable. Among numerous characteristics that are effected by a modification in the permeability of the crest, this report looks specifically into three separate aspects: the design level changes that are caused by modifications in the permeability of the crest, a comparison of the total and sector-wise overtopping discharges and finally the differences in spatial overtopping intensities between the two.
By looking into two well-known overtopping design guidelines for overtopping, namely, Owen and Eurotop, this report aims to look at the differences it would make in designing a breakwater with either an impermeable or a permeable crest. This is done by building a breakwater model in a wave flume and comparing it with the existing guidelines and assessing the changes that best represent the modified model.
It is also important to observe how this physical modification of the crest affects the overtopping discharges and spatial overtopping intensities behind the crest of the breakwater. This will be relevant for designers or contractors tasked to make changes to an existing breakwater that results in its crest becoming impermeable. An insight into the overtopping discharges and intensities will be extremely useful to be able to predict the overall changes and cater for them.
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HISGIS: golvenmodel HISWA onder GIS pakket ARC/INFO
HISWA is een tweedimensionaal golvenmodel, dat de gebruiker in staat stelt diverse golfgegevens, zoals significante golfhoogte, periode en golfrichting, voor een bepaald modelgebied te bepalen. Op dit moment biedt HISWA al faciliteiten om pre- en postprocessing uit te voeren (zij het in beperkte mate). Onder de gebruikers echter is er behoefte aan meer en uitgebreidere mogelijkheden. Door de functionaliteiten op het gebied van weergave en analyse van gegevens, leent een GIS (Geografisch Informatie Systeem) zich uitstekend voor pre- en post-processing doeleinden. Het doel van het project is het koppelen van HISWA aan een GIS-pakket, en wel op een dusdanige manier dat een gebruikersvriendelijke schil ontstaat, waarbinnen een HISWA berekening kan worden uitgevoerd en tevens van de functionaliteiten van het GIS-pakket gebruik kan worden gemaakt voor pre- en post-processing doeleinden. Aan de hand van de resultaten van een vragenformulier zijn de eisen en wensen van de huidige HISWA-gebruiker, met betrekking tot bovengenoemde koppeling, geïnventariseerd. Tevens zijn uit deze resultaten conclusies getrokken wat betreft de benodigde functionaliteiten van het te gebruiken GIS-pakket. Er is, voorafgaand aan het afstudeerproject, gekozen voor 's werelds meest gebruikte en veruit bekendste GIS-pakket, ARC/INFO. Uit onderzoek, uitgevoerd tijdens het afstudeerproject, blijkt, dat het pakket over vrijwel alle benodigde functionaliteiten beschikt. In ARC/INFO's macrotaai AML (ARC/INFO Macro Language) is een volledig menugestuurde applicatie ontwikkeld, genaamd HISGIS. De applicatie HISGIS bestaat uit een viertal delen, te weten het hoofdprogramma, een 'Pre-processing module', een 'Calculation module' en een 'Post-processing module'. In het hoofdprogramma kunnen de drie modules met behulp van een menu worden aangeroepen.
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Transport van stortsteen door golven en stroming
Een belangrijk aspect bij het bepalen van de resulterende schuifspanning is de niet-lineaire interactie tussen golven en stroming. De grenslagen van de golven en de stroming beinvloeden elkaar wederzijds, waardoor de gemiddelde schuifspanning en de maximale schuifspanning voor de combinatie van golven en stroming groter zijn dan kan worden verwacht op grond van een lineaire interactie tussen golven en stroming. De experimenten zijn uitgevoerd in de zogenaamde "lange speurwerkgoot" van het laboratorium voor vloeistofmechanica. In de goot zijn twee meetgebieden aangebracht van 0,5 bij 0,5 m2. De meetgebieden zijn onderverdeeld in 10 gekleurde stroken van 5 cm breedte. De nominale diameter van de steentjes bedraagt 5,45 mm. Het uitgangspunt van het experimentele gedeelte van dit onderzoek is dat de verplaatsingen veroorzaakt moeten worden door de combinatie van golven en stroming. Daarom is de stroomsnelheid bewust laag gehouden, d.w.z. de mobiliteitsparameter (q-t) van de stroming varieert van 0,007 tot 0,021. Per stroomsnelheidserie is de golfhoogte gevarieerd van circa 0,05 m tot 0,15 m, bij een periode van 1,1 s. De periode van de golf is beperkt gevarieerd: er is aan serie experimenten uitgevoerd met een periode van 1 s. Wanneer de meetdata van de pick-up en het transport uit het experimentele onderzoek worden uitgezet tegen de gemiddelde gecombineerde mobiliteitsparameter t.g.v. van de golf-stroming interactie, dan blijkt dat de meetdata een puntenwolk vormen waaruit een trend afgeleid kan worden. In het onderzoek is een aantal formules afgeleid die de pick-up en het transport van stortsteen door een belastingscombinatie van golven en stroming beschrijven. Echter de spreiding van de meetwaarden t.o.v. de in dit onderzoek gevonden formules is zo groot dat het niet onomstotelijk vaststaat dat de gemiddelde gecombineerde schuifspanning de juiste maat voor de belasting op de steentjes is. De theorie van Grant en Madsen blijkt een goede theorie te zijn om de belasting op de bodem te bepalen; zowel in de gevonden pick-up formule als in de gevonden transportformule wordt de gemiddelde gecombineerde mobiliteitsparameter bepaald met de golf-stroming interactietheorie van Grant en Madsen. Bij het afleiden van een transportformule bleek dat er geen duidelijke voorkeur voor de golf-stroming interactietheorie van Grant en Madsen is. Ook wanneer de meetwaarden van de transporten worden uitgezet tegen de gemiddelde gecombineerde mobiliteitsparameter, berekend volgens de theorie van Fredsoe, blijkt dat de meetdata gaan samenvallen.
Wanneer de gemiddelde gecombineerde mobiliteitsparameter volgens de theorie van Bijker wordt berekend, is er geen verband tussen belasting en verplaatsingen van steentjes af te leiden. Naast de vraag of de gemiddelde gecombineerde schuifspanning echt de juiste parameter is om de belasting in deze complexe belastingssituatie weer te geven, kleven er aan de resultaten van dit onderzoek kleven nog drie grote nadelen: 1. De afgeleide formules zijn beperkt geldig doordat een aantal relevante variabelen, zoals de diameter en vorm van het bodemmateriaal, de periode van de golven en de waterdiepte, niet of nauwelijks gevarieerd zijn. 2. De afgeleide formules zijn beperkt toepasbaar doordat het onderzoeksbereik niet groot genoeg is. Er zijn slechts meetwaarden bekend tot een gemiddelde gecombineerde mobiliteitsparameter van 0,035. Het interessegebied voor het ontwerpen van de toplaag van een bodemverdediging ligt bij waarden rondom de Shieldsparameter. 3. De resultaten hebben een geringe betrouwbaarheid. Het werkelijk optredende transport kan bij een lage gemiddelde gecombineerde mobiliteitsparameter tot 80% afwijken van de waarde die met de gevonden transportformules wordt voorspeld. Dit wordt veroorzaakt door het geringe aantal steentjes dat er bij zo een lage belasting verplaatst. Deze drie bezwaren zorgen ervoor dat de in dit onderzoek gevonden formules beperkt bruikbaar zijn voor het ontwerpen van de toplaag van de bodemverdediging, wanneer deze wordt belast door een combinatie van golven en stroming.
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[Abstract]
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