4.1 : A wave with a wavelength of 50 m is incident on a vertical wall. What is the reflection coefficient?
Solution: Using the breaking wave criterion, we can calculate the breaking wave height: $H_b = 0.42 \times 5 = 2.1$ m.
Solution: A water wave is a surface wave that travels through the ocean, caused by wind friction, while a tsunami is a series of ocean waves with extremely long wavelengths, caused by displacement of a large volume of water. Solution: A water wave is a surface wave
Solution: The reflection coefficient for a vertical wall is: $K_r = -1$.
5.2 : A wave with a wave height of 2 m and a wavelength of 50 m is running up on a beach with a slope of 1:10. What is the run-up height? What is the run-up height
Solution: The boundary conditions are: (1) the kinematic free surface boundary condition, (2) the dynamic free surface boundary condition, and (3) the bottom boundary condition.
2.2 : What are the boundary conditions for a water wave problem? Solution: Using the Sommerfeld-Malyuzhinets solution
Solution: Using the dispersion relation, we can calculate the wave speed: $c = \sqrt{\frac{g \lambda}{2 \pi} \tanh{\frac{2 \pi d}{\lambda}}} = \sqrt{\frac{9.81 \times 100}{2 \pi} \tanh{\frac{2 \pi \times 10}{100}}} = 9.85$ m/s.
4.2 : A wave is diffracted around a semi-infinite breakwater. What is the diffraction coefficient?
Solution: Using the Sommerfeld-Malyuzhinets solution, we can calculate the diffraction coefficient: $K_d = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} e^{i k r \cos{\theta}} d \theta$.