CRM 4022 Coastal Engineering: Ocean Waves II

Study Notes

Fluid is considered homogeneous and incompressible with constant density.
Surface tension is ignored for simplicity in calculations.
The Coriolis effect has no impact on wave motion under this theory.
Pressure is uniform and constant at the free surface of the fluid.
Assumes ideal fluid conditions, meaning it is devoid of viscosity.
Waves do not interact with other motions in the water.
The bed is modeled as a horizontal, fixed, impermeable boundary, leading to zero vertical velocity at the bed.
Waves have small amplitudes, maintaining the same form over time and space.
Only two-dimensional (plane) or low-crested waves are considered.

Longer waves travel at higher speeds compared to shorter waves.
Incremental increases in period (T) result in significant increases in wavelength (L).
Long waves (swell) retain energy well and travel faster, while short waves lose energy quickly before reaching shore.
Specific values related to wave properties: k = 0.016, Kp = 0.791, P max = 179 kPa.

Surface waves depict local fluid velocities and accelerations in both horizontal and vertical directions.

Linear superposition is applied through Fourier transformation to analyze wave patterns.
The total energy of waves is defined via the energy density function:
- Total Energy = ρg ∫₀^∞ S(ω) dω
Wave spectrum energy density relationship given as:
- S(ω) = 1/(2 ∆ω) A²/ω

Long-term datasets are typically analyzed over periods, such as 34.9 years using hourly data.
The Weibull distribution is commonly used to model wave heights and frequencies.