130 lines
6.5 KiB
TeX
130 lines
6.5 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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\section{Separating incident and reflected components from wave buoy data}
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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,
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and they can generally be categorised in two types of methods: array methods
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and PUV methods \parencite{inch2016accurate}. Array methods rely on the use of
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multiple measurement points of water level to extracted the incident and
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reflected waves, while PUV methods use colocated pressure and velocity
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measurements to separate incident and reflected components of the 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
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noise, non-linear interactions, and probe spacing. The admissible frequency
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range could also be widened. A similar method was proposed by
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\textcite{gaillard1980}. The accuracy of the method for the estimation of
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incident and reflected wave components was once again highlighted, while the
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importance of adequate positioning of the gauges 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. However, they require at least two wave gauges to be used.
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That means that in some situations such as the Saint-Jean-de-Luz event of 2017,
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other methods are needed since only one field measurement location is
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available.
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\subsection{PUV methods}
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\begin{itemize}
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\item ?? \cite{guza1977resonant}: model of the surf zone as a standing wave
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combined with a progressive wave. Accurate results of surface elevation and
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runup for reflectivities over 0.3.
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\item ?? \cite{guza1984}:
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\item \cite{tatavarti1989incoming}: Decompose colocated random field
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measurements of wave elevation and currenct velocity into incoming and
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outgoing components. Less sensitive to noise.
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\item \cite{kubota1990}: comparison between different wave theories:
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quasi-nonlinear long-wave theory gave the best results.
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\item \cite{walton1992}: application to beaches, possibility to have higher
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reflected energy than incident energy.
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\item \cite{hughes1993}: colocated horizontal and vertical velocities or
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horizontal velocity and surface elevation. Validation for full reflection
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of irregular non breaking waves.
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\item \cite{huntley1999use}: principal component analysis technique to avoid
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noise-induced bias.
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\item \cite{sheremet2002observations}:
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\end{itemize}
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\section{Modeling wave impact on a breakwater}
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\subsection{SPH models}
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\subsection{VARANS models}
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\section{Modeling block displacement}
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