CRM 4022 Coastal Engineering: Ocean Waves II

Questions and Answers

Fluid is homogenous and compressible in small amplitude wave theory.

False

Which of the following assumptions is not part of the small amplitude/first order/Airy wave theory?

Waves are plane or low crested.

Surface tension is significant. (correct)

Pressure at the free surface is uniform and constant.

Fluid is ideal and lacks viscosity.

What happens to longer waves compared to shorter waves in terms of travel speed?

Longer waves travel faster than shorter waves.

In small amplitude wave theory, the wave amplitude is ______.

small Signup and view all the answers

What is the implication of a horizontal, fixed, impermeable boundary on the vertical velocity at the bed?

The vertical velocity at the bed is zero. Signup and view all the answers

Match the distributions with their occurrences:

0-1 = 0.15 1-2 = 0.24 2-3 = 0.29 3-4 = 0.21 4-5 = 0.09 5-6 = 0.03 Signup and view all the answers

What is the relationship between wave period (T) and wavelength (L) in small amplitude wave theory?

Small increases in T are associated with large increases in L. Signup and view all the answers

What does the symbol $k$ equal in the context provided?

0.016 Signup and view all the answers

Study Notes

Small Amplitude/First Order/Airy Wave Theory

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.

Wave Propagation Characteristics

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.

Motion in Surface Waves

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

Irregular Waves and Probability Distribution

The occurrence of irregular waves varies across different height intervals, showing a distribution of wave frequencies:
- 0-1 m: 50 occurrences (15%)
- 1-2 m: 80 occurrences (24%)
- 2-3 m: 100 occurrences (29%)
- 3-4 m: 70 occurrences (21%)
- 4-5 m: 30 occurrences (9%)
- 5-6 m: 10 occurrences (3%)

Fourier Transformation and Energy Density

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

Data Utilization

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.

Description

This quiz covers key concepts in coastal engineering, specifically focusing on the second part of wave theory as taught in CRM 4022 at Ocean University of Sri Lanka. Participants will explore the characteristics of small amplitude waves and the assumptions made in the Airy wave theory. Ideal for students looking to deepen their understanding of wave dynamics in ocean engineering.