235 lines
11 KiB
TeX
235 lines
11 KiB
TeX
\chapter{Literature Review}
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In this chapter, literature relevant to the present study will be reviewed.
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Three sections will be detailled: the separation of incident and reflected
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components from wave measurements, the modelisation of wave impacts on a
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rubble-mound breakwater, and the modelisation of block displacement by wave
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impacts.
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\section{Separating incident and reflected components from wave buoy data}
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\subsection{Introduction}
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The separation of incident and reflected waves is a crucial step in numerically
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modeling a sea state. Using the raw data from a buoy as the input of a wave
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model will lead to incorrect results in the domain as the flow velocity at the
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boundary will not be correctly generated.
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Several methods exist to extract incident and reflected components in measured
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sea states, and they can generally be categorised in two types of methods:
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array methods and PUV methods \parencite{inch2016accurate}. Array methods rely
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on the use of multiple measurement points of water level to extracted the
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incident and reflected waves, while PUV methods use co-located pressure and
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velocity measurements to separate incident and reflected components of the
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signal.
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\subsection{Array methods}
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\subsubsection{2-point methods}
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Array methods were developped as a way to isolate incident and reflected wave
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components using multiple wave records.
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\textcite{goda1977estimation,morden1977decomposition} used two wave gauges
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located along the wave direction, along with spectral analysis, in order to
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extract the incident and reflected wave spectra. Their work is based on the
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earlier work of \textcite{thornton1972spectral}. \textcite{goda1977estimation}
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analyzed the wave spectrum components using the Fast Fourier Transform, and
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suggests that this method is adequate for studies in wave flumes. They noted
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that this method provides diverging results for gauge spacings that are
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multiples of half of the wave length. \textcite{morden1977decomposition}
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applies this technique to a field study, where the sea state is wind generated.
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\textcite{morden1977decomposition} showed that, using appropriate spectral
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analysis methods along with linear wave theory, the decomposition of the sea
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state into incident and reflected waves is accurate. A relation between the
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maximum obtainable frequency and the distance between the sensors is provided.
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According to \textcite{morden1977decomposition}, the only needed knowledge on
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the wave environment is that wave frequencies are not modified by the
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reflection process.
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\subsubsection{3-point methods}
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In order to alleviate the limitations from the 2-point methods,
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\textcite{mansard1980measurement} introduced a 3-point method. The addition of
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a supplementary measurement point along with the use of a least-squares method
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most importantly provided less sensitivity to noise, non-linear interactions,
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and probe spacing. The admissible frequency range could also be widened. A
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similar method was proposed by \textcite{gaillard1980}. The accuracy of the
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method for the estimation of incident and reflected wave components was once
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again highlighted, while the importance of adequate positioning of the gauges
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was still noted.
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\subsubsection{Time-domain method}
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\textcite{frigaard1995time} presented a time-domain method for reflected and
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incident wave separation. This method, called SIRW method, used discrete
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filters to extract the incident component of an irregular wave field. The
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results were as accurate as with the method proposed by
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\cite{goda1977estimation}, while singularity points are better accounted for.
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The main advantage of the SIRW method is that it works in the time-domain,
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meaning that real time computations can be performed.
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\textcite{frigaard1995time} also mentions the possibility of replacing one of
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the wave gauges by a velocity meters to prevent singularities.
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This method was improved by \textcite{baldock1999separation} in order to
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account for arbitrary bathymetry. Linear theory is used to compute shoaling on
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the varying bathymetry. Resulting errors in the computed reflection coefficient
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are low for large reflection coefficients, but increase with lower
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coefficients. The neglect of shoaling can lead to important error in many
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cases. The presented method could also be extended to three-dimensionnal waves
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and bathymetry by considering the influence of refraction.
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\subsubsection{Further improvements}
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Further additions were made to array methods. \textcite{suh2001separation}
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developped a method taking constant current into account to separate incident
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and reflected waves. This method relies on two or more gauges, using a least
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squares method. Results are very accurate in the absence of noise, but a small
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amount of error appears when noise is added.
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\textcite{inch2016accurate} noticed that the presence of noise lead to
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overestimation of reflection coefficient. The creation of bias lookup tables is
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proposed in order to account for noise-induced error in reflection coefficient
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estimations.
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\textcite{andersen2017estimation,roge2019estimation} later proposed
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improvements to account for highly non-linear regular and irregular waves
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respectively. The improved method provides very accurate results for highly
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non-linear waves, but are expected to be unreliable in the case of steep
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seabeds, as shoaling is not part of the underlying model.
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\subsubsection{Conclusion}
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Array methods have been developped enough to provide accurate results in a wide
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range of situations. Sensibility to noise has been reduced, and the influence
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of shoaling has been considered. Those methods can also be applied to irregular
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non-linear waves.
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However, they require at least two wave gauges to be used. That means that in
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some situations such as the Saint-Jean-de-Luz event of 2017, other methods are
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needed since only one field measurement location is available.
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\subsection{PUV methods}
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The goal of PUV methods is to decompose the wave field into incident and
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reflected waves using co-located wave elevation and flow velocity measurements
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\parencite{tatavarti1989incoming}. \textcite{tatavarti1989incoming} presented a
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detailled analysis of separation of incoming and outging waves using co-located
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velocity and wave height sensors. Their method allows to obtain the reflection
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coefficient relative to frequency, as well as to separate incident and
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reflected wave components. Compared to array methods, this method also strongly
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reduces the influence of noise.
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\textcite{kubota1990} studied the influence of the considered wave theory on
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incident and reflected wave separation. Three methods, based on linear
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long-wave theory, small-amplitude wave theory and quasi-nonlinear long-wave
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theory respectiveley were developped and compared. The results show that the
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quasi-nonlinear approach gave the most accurate results.
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%\textcite{walton1992} applied a separation method based on co-located pressure
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%and velocity measurements on field, studying two natural beaches. This study
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%showed that reflection is not significant on natural beaches. Additionnaly,
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%the method that is used allowed for larger reflected energy than incident
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%energy.
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Research by \textcite{hughes1993} showed how co-located horizontal velocity and
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vertical velocity (or pressure) sensors can be used to extract incident and
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reflected wave spectra. Their method is based on frequency domain linear
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theory, and provided accurate results for full reflection of irregular
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non-breaking waves. Low-reflection scenarii were evaluated against the results
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from \textcite{goda1977estimation}, and showed good agreement between both
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methods. \textcite{hughes1993} also highlights that reflection estimates are
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unreliable for higher frequency, where coherency between the two measured
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series is lower.
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Following the work of \textcite{tatavarti1989incoming},
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\textcite{huntley1999use} showed how principal component analysis can alleviate
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noise-induced bias in reflection coefficient calculations compared to
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time-domain analysis. They also stuied the influence of imperfect collocation
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of the sensors, showing that the time delay between sensors leads to a peak in
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the reflection coefficient at a frequency related to this time delta.
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%%% TODO? %%%
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% \cite{sheremet2002observations}
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\subsection{Conclusion}
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Numerous methods have been developped in order to separate incident and
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reflected components from wave measurements. Array methods rely on the use of
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multiple, generally aligned, wave gauges, while PUV methods rely on the use of
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co-located sensors, generally a wave height sensor and a horizontal velocity
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sensor. Array methods generally have the advantage of being more cost-effective
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to implement, as the cost of reliable velocity measurement devices can be
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important \parencite{hughes1993}. Nevertheless, PUV methods are generally more
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accurate regarding noise, varying bathymetry, and can be setup closer to
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reflective surfaces \parencite{hughes1993,inch2016accurate}.
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In the case of the 2017 event on the Artha breakwater, the results from a
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single wave gauge are available, which means that the array methods are not
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applicable. A PUV method \parencite{tatavarti1989incoming,huntley1999use}
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should then be used to evaluate the reflection coefficient of the Artha
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breakwater and to separate the incident and reflected wave components from the
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measured data.
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\section{Modelling wave impact on a breakwater}
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Modelling rubble-mound breakwaters such as the Artha breakwater requires
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complex considerations on several aspects. First of all, an accurate of the
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fluid's behavior in the porous armour of the breakwater is necessary. Then,
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adequate turbulence models are needed in order to obtain accurate results.
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Several types of models have been developped that can be used to study breaking
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wave flow on a porous breakwater.
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\subsection{SPH models}
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Smoothed-Particle Hydrodynamics (SPH) models rely on a Lagrangian
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representation of the fluid.
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\subsubsection{Porosity modelling}
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\cite{jiang2007mesoscale}
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\cite{jutzi2008numerical}
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\cite{shao2010}
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\cite{altomare2014numerical}
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\cite{kunz2016study}
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\textbf{\cite{ren2016improved}}
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\cite{pahar2016modeling}
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\cite{peng2017multiphase}
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\cite{wen20183d}
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\cite{kazemi2020sph}
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\subsubsection{Wave generation}
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\cite{yim2008numerical}
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\cite{altomare2017long}
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\cite{wen2018non}
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\subsection{VARANS models}
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\cite{van1995wave,troch1999development}
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COBRAS \parencite{liu1999numerical}: spatially averaged RANS
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with $k-\varepsilon$ turbulence model. Drag forces modeled by empirical linear
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and non-linear friction terms; \cite{hsu2002numerical}: introduced VARANS in
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order to account for small scale turbulence inside the porous media.
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->
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COBRAS-UC/IH2VOF \parencite{losada2008numerical,lara2008wave}: VOF VARANS (2D);
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refactor of COBRAS code, with improved wave generation, improvement of input
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and output data.
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->
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IH3VOF \parencite{del2011three}: 3D VOF VARANS, updated porous media equations,
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optimization of accuracy vs computation requirements, specific boundary
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conditions, validation. Adding SST model.
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->
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IHFOAM/olaFlow \parencite{higuera2015application}: Rederivation of
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\cite{del2011three}, add time-varying porosity; Improvement to wave generation
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and absorption; implementation in OpenFOAM; extensive validation; application
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to real coastal structures.
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\cite{vieira2021novel}: Use of artificial neural networks to determine porosity
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parameter for VOF VARANS model.
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\subsection{Other}
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BEM: \cite{hall1994boundary,koley2020numerical}
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\section{Modeling block displacement}
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