Linear Wave Theory (10pt)

1
Linear Wave Theory (10pt)

• The maximum vertical particle velocity occurs at
• (1) Crest (2) trough (3) crossing-point

2
capillary waves (10pt)

• What is the primary restoring force for capillary
  waves?
• Coriolis force
• Gravity force
• Surface tension

3
Tsunamis (10pt)

• What is the ratio of tsunami celerity
• at 400m waterdepth to
• that at 40m waterdepth?

4
Elastic Wave on Tensioned String (15pt)

• When Tension300N, Mass/length3kg/m,
• Circular frequency10rad/s
• Find the corresponding wavelength!

5
Airys Linear Wave Theory (15pt)

• Wave length120m, water depth15m
• What is the wave period?

6
Celerity Group Velocity (15pt)

• If a sinusoidal wave has the following dispersion
  relation between circular frequency w and wave
  number k
• w3k
• Find its celerity and group velocity.

7
Celerity Group Velocity (15pt)

• When wavelength80m at 6m water depth, what is
  the group velocity?

8
particle velocity (20pt)

• When wavelength80m at 6m water depth (same as
  previous question), what is the maximum
  horizontal particle velocity at the crest of 2-m
  wave amplitude?

9
Wave energy (20pt)

• What is the total wave energy in one wavelength
  and along 1-km crest line in deep water for
• H4m
• T11s

10
Wave Power (20pt)

• What is wave power in deep water per unit width
  of crest line?
• H4m
• T11s

11
Encounter Frequency Doppler Effect (20pt)

• If ship speed is 6m/s and advancing in the same
  direction as a linear wave of length120m in deep
  water,
• What is the encounter wave frequency observed
  from the ship?

12
Partial Standing Wave (30pt)

• When maximum and minimum free-surface elevations
  above MWL are
• 1m and 0.2m and the distance between them is 30m
• Find wave length and reflection coefficient!

13
Perfect Standing Wave (30pt)

• In Deepwater,
• Elevation of anti-node above MWL4m
• Wave period10s
• What is the magnitude of horizontal particle
  velocity 2m below the node?

14
Particle Orbit of Linear Wave (25pt)

• Wave length100m, water depth10m, wave height2m
• What is the major semi-axis (longer radius) of
  the elliptical orbit at z0?

15
Pressure (30pt)

• Wave length100m, water depth10m, wave height2m
• (same as previous question)
• What is the static and dynamic pressure magnitude
  3m below MWL?

16
Shoaling (30pt)

• In case of normal incidence and mild-slope seabed
  (neglect refraction and reflection)
• What is the new wavelength and wave height at
  depth7m for 11s deepwater wave.