1.1 : What is the difference between a water wave and a tsunami?
Solution: The main assumptions made in water wave mechanics are: (1) the fluid is incompressible, (2) the fluid is inviscid, (3) the flow is irrotational, and (4) the wave height is small compared to the wavelength.
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
2.2 : What are the boundary conditions for a water wave problem?
Solution: The Laplace equation is derived from the continuity equation and the assumption of irrotational flow: $\nabla^2 \phi = 0$, where $\phi$ is the velocity potential. Solution: Using the run-up formula, we can calculate
Solution: Using the run-up formula, we can calculate the run-up height: $R = \frac{H}{\tan{\beta}} = \frac{2}{0.1} = 20$ m.
Solution: The reflection coefficient for a vertical wall is: $K_r = -1$. Solution: Using the run-up formula
Solution: Using the breaking wave criterion, we can calculate the breaking wave height: $H_b = 0.42 \times 5 = 2.1$ m.