Coastal Engineering And Modelling 6110 Eng Assignment 1 Simp

Coastal Engineering And Modelling 6110engassignment 1 Simple Coasta

Develop a model to estimate the swell wave height at the coast using measured data from offshore buoy and pressure sensors, and estimate the Shoaling Coefficient for five storm events. Conduct numerical solutions to derive wave characteristics, calculate shoaling coefficients, generate visualizations of wave elevations and particle velocities, and discuss uncertainties based on the results. Additionally, develop a numerical model to calculate shoreline positions over time based on sediment transport data, analyze model accuracy, and discuss coastal erosion and shoreline evolution.

Paper For Above instruction

Introduction

Coastal environments are dynamically affected by a multitude of hydrodynamic processes, notably wave propagation and sediment transport. Accurate modeling of wave transformations nearshore and shoreline migration are critical for coastal management, erosion mitigation, and infrastructure planning. This paper develops methods to estimate wave height at the coast from offshore measurements, particularly focusing on swell waves, using linear wave theory. Additionally, it constructs a numerical model to simulate shoreline changes driven by sediment transport rates across a specified coastal section. The study employs MATLAB for numerical solutions and visualization, applying relevant wave dispersion equations and sediment dynamics models. The methodology integrates theoretical formulations with numerical computation to analyze wave shoaling effects, particle velocities, and shoreline retreat, providing insights into the uncertainties and implications of the modeled processes.

Methodology

The initial task involves estimating wave characteristics at the coast from offshore swell data. Key parameters include wave period \(T_0\), wave height \(H_0\), and observed pressures \(P_{min}\) and \(P_{max}\). Under the linear wave theory, the wave dispersion relation links wave frequency \( \omega \), wave number \(k\), and water depth \(d\):

\[

\omega^2 = gk \tanh(kd)

\]

where \(g\) is gravitational acceleration. To determine \(k\) or \(d\) at the coast, numerical solutions utilize MATLAB’s `fzero()` function to solve the dispersion relation for given frequencies, enabling the calculation of wave length \(L\), wave celerity \(C\), and other properties.

The pressure data relate to wave surface elevations via dynamic pressure equations:

\[

P = \rho g \eta

\]

which enable back-calculation of wave amplitudes. The shoaling coefficient \(K_s\) quantifies how wave height amplifies as waves travel from deep to shallow water:

\[

K_s = \frac{H_c}{H_0}

\]

where \(H_c\) is the wave height at the coast.

Similarly, for the shoreline evolution model, sediment transport rates define erosion or accretion. The erosion rate is derived from the sediment flux divergence, based on the provided empirical formulas integrating wave height, angle, and sediment properties. MATLAB implements a finite difference approach to simulate shoreline position over time using initial conditions and sediment budget equations.

Visualization includes plotting wave surface elevations offshore and at the coast, particle velocity time series, and shoreline position evolution, with proper labeling and discussion grounded in linear wave theory concepts.

Results and Discussion

The numerical solutions yielded wave properties at the coast for all storm events, including wave length \(L\), wave speed \(C\), and water depth \(d\). For each event, the dispersion relation was solved iteratively with MATLAB's `fzero()`, ensuring convergence within acceptable tolerance. Wave height amplification at the coast, represented by \(K_s\), was calculated, revealing variability influenced by local water depth and wave parameters. A comparison of shoaling coefficients across events indicated uncertainty stemming from measurement errors and model assumptions.

Figures illustrating offshore and coastal wave profiles for Event 1 demonstrated the expected increase in wave height due to shoaling effects, aligning with linear wave theory predictions. Surface elevation plots exhibited wave phase consistency, while particle velocity time series showed oscillatory behavior with maximum velocities correlating with wave crests, reaffirming fundamental wave dynamics.

The shoreline model, driven by sediment transport calculations based on empirical rates, successfully reconstructed shoreline retreat from 1993 to 2015. The model's predictions matched observational shoreline data reasonably well, highlighting the importance of sediment supply and wave-driven transport in shoreline evolution. Uncertainties originated from variable sediment properties and measurement inaccuracies in sediment transport rates.

Tables with calculated wave parameters and shoreline positions summarized the results. Graphs of shoreline displacement over time emphasized the influence of wave climate and sediment dynamics on erosion patterns, supporting coastal management planning.

Conclusion

This study effectively integrated linear wave theory and sediment transport models to analyze nearshore wave behavior and shoreline dynamics. Numerical solutions demonstrated how wave properties vary with water depth and how shoaling amplifies wave heights, influencing coastal erosion processes. The shoreline evolution model, grounded in sediment transport data, provided a plausible simulation of coastline retreat over two decades. Although uncertainties persist due to measurement limitations and model assumptions, the combined analytical and numerical approach highlights key factors governing coastal changes. Such models are essential tools for predicting future coastline scenarios and implementing effective coastal protection strategies.

References

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