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Temporal and spectral analysis of simulated and experimental Boussinesq type waves
Author(s)
Scarrott, Jordan Ross
Date Issued
2024
Type
Thesis
Publisher
Cape Peninsula University of Technology
Abstract
In this project we are interested in using computers to predict the characteristics
of ocean waves where they meet the shore. Waves in the ocean play
an important role in a number of areas as follows: Out in the deep sea they
impact shipping and fishing. The breaking of waves along the coast results
in erosion and beach line changes. The breaking of waves also creates huge
forces on shoreline structures and can be very destructive. Thus a knowledge
of these waves and their characteristics is useful for beach management and
protecting coastal structures and harbours.
In order for numerical models to be valid, they must be comparable to
real world experimental equivalents. This is particularly true for complex
phenomena like Boussinesq beach waves. The Boussinesq equation is highly
nonlinear and is further complicated by the boundary conditions that need
to be satisfied. In this work we aim to numerically solve the equations for
water waves propagating along a narrow and long tank in which a sloping
bottom is introduced at one end. The purpose of the sloping bottom is to
create/simulate breaking waves. By doing so we aim to determine the domain
of validity for the chosen numerical scheme.
As a precursor for solving the Boussinesq equation, we first attempt to
numerically solve the classical one dimensional wave equation, followed by
the numerical solution of the Korteweg-de Vries (KdV) equation. In solving
these two partial di!erential equations we set the scene for the more complex
Boussinesq equation. In solving each of these equations we set up the discretisation
procedure, followed by actual implementation of the discretised
equation using MATLAB.
In the numerical solution of the one dimensional wave equation and the
KdV equation, the accuracy of the numerical techniques is assessed by comparing
them to analytical solutions or results published in the open literature.
In the case of the Boussinesq equation, the accuracy of the results are assessed
by comparing them to a real experiment conducted in a wave tank.
In both the numerical and experimental cases, we examine the changes in
wave profile, wave speed, and spectral content of the waves as they move from water of constant depth into a region containing a sloping beach where
breaking occurred.
of ocean waves where they meet the shore. Waves in the ocean play
an important role in a number of areas as follows: Out in the deep sea they
impact shipping and fishing. The breaking of waves along the coast results
in erosion and beach line changes. The breaking of waves also creates huge
forces on shoreline structures and can be very destructive. Thus a knowledge
of these waves and their characteristics is useful for beach management and
protecting coastal structures and harbours.
In order for numerical models to be valid, they must be comparable to
real world experimental equivalents. This is particularly true for complex
phenomena like Boussinesq beach waves. The Boussinesq equation is highly
nonlinear and is further complicated by the boundary conditions that need
to be satisfied. In this work we aim to numerically solve the equations for
water waves propagating along a narrow and long tank in which a sloping
bottom is introduced at one end. The purpose of the sloping bottom is to
create/simulate breaking waves. By doing so we aim to determine the domain
of validity for the chosen numerical scheme.
As a precursor for solving the Boussinesq equation, we first attempt to
numerically solve the classical one dimensional wave equation, followed by
the numerical solution of the Korteweg-de Vries (KdV) equation. In solving
these two partial di!erential equations we set the scene for the more complex
Boussinesq equation. In solving each of these equations we set up the discretisation
procedure, followed by actual implementation of the discretised
equation using MATLAB.
In the numerical solution of the one dimensional wave equation and the
KdV equation, the accuracy of the numerical techniques is assessed by comparing
them to analytical solutions or results published in the open literature.
In the case of the Boussinesq equation, the accuracy of the results are assessed
by comparing them to a real experiment conducted in a wave tank.
In both the numerical and experimental cases, we examine the changes in
wave profile, wave speed, and spectral content of the waves as they move from water of constant depth into a region containing a sloping beach where
breaking occurred.
Additional information
Thesis (MEng (Electrical Engineering))--Cape Peninsula University of Technology, 2024
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