Wave Theory Problem Solution - Environmental Engineering, Semester 1

This assignment solution addresses a wave theory problem in environmental engineering, focusing on wave characteristics and behavior. The solution includes two parts: the first analyzes waves incident on a straight beach, calculating wave height and wavelength under deep-water conditions and for varying water depths. The second part explores the applicability of Stokes and Cnoidal wave theories based on given parameters like wave height, period, and water depth. The solution utilizes linear wave theory to determine appropriate wave models and provides a comprehensive understanding of wave dynamics in different scenarios, crucial for environmental engineering applications.

Problem 2-1. (55 points)
Part 1
Waves normally incident on a straight gently sloping beach are recorded to have a wave height of 1.2m
and a wave period of 7.5s in water depths of 4m. Assume linear wave theory is valid and neglect
reflection and energy dissipation.
1. What is the wave height and wave length in deep water condition?
Part 2
Waves with wave height 0.8m and a wave period of 7.5s are obliquely incident on a long straight beach
of gently slow. The angle of incidence in deep water is 33°.
2. Use linear wave theory and estimate the wave height and angle of incidence for a water depth of 8m
and 4m. Compare the results with that of Part 1.
Problem 2-2. (45 points)
Determine whether Stokes wave or Cnoidal wave should be used in the following conditions. (Use linear
wave theory to calculate Ursell parameter). (The choice of transition from one form of wave theory to
another depends on the individual problem.)
1. Wave height: 2.5 m Wave period: 7 s Water depth: 15 m
2. Wave height: 2.5 m Wave period: 7 s Water depth: 5 m
3. Wave height: 2.5 m Wave period: 4 s Water depth: 5 m
4. Wave height: 2.5 m Wave period: 4 s Water depth: 10m