a. To learn the terminology for describing surface gravity waves.

b. To understand deep water waves and their interactions with each other.

c. To understand shallow water waves and their interactions with topography.

2. General Definitions:

Waves are caused by a generating force that moves the surface from its undisturbed level, and a restoring force that returns it.

Generating Forces: wind
physical disturbances (earthquakes, landslides, ships)

Restoring Forces: surface tension - small capillary waves
gravity - larger gravity waves

Progressive Waves: Travel in a particular direction.

Standing Waves: Remain at a fixed location.

Forced Waves: Still under the influence of the forcing.

Free Waves: Have propagated out of the region of forcing.

2. Wave Anatomy Definitions:

Equilibrium surface - undisturbed state
Crest - highest point
Trough - lowest point
Wavelength (L) - horizontal distance between 2 crests or troughs.
Height (H) - vertical distance between a crest and trough.
Amplitude (A) - vertical distance from equilibrium surface to crest or trough (= H/2).
Steepness (S) - height divided by wavelength.
Period (T) - Time for 1 wavelength to propagate past an observation point.
Phase Speed (C) - speed at which individual crests and troughs propagate.
Phase Speed: C=L/T
Group Speed (V) - speed at which a group of waves propagates.
Particle Orbit - motion of a water particle beneath a wave.

3. Wave Height Dependence:

Factors that determine wave height:
1) Wind Speed
2) Wind Duration
3) Fetch (distance over which the wind blows)

Increases in these increase height.
Energy is proportional to amplitude squared.

4. Wave Steepness Limitation:

S = H/L
For Breaking S > 1/7 - wave breaks.

5. Wave Period Constraint:

Wave period remains constant over its lifetime.
"Conservation of Wave Crests"

6. Deep Water Waves (D > L/2)

Particle orbits (deepwater):
circular, decay exponentially with depth
negligible below a depth of L/2
particles move forward with crest, backward with trough.

Wavelength: L = (g/2p) T² = 1.56 T²
for T=10 sec, L=156 m.

Phase Speed: C= L/T = (g/2p) T = 1.56 T
for T=10 sec, C= 15.6 m/sec.

Deepwater Waves are Dispersive:
Longer periods have longer wavelengths that travel faster.

At a storm center, waves of all periods are generated. Far away from the storm, the longer faster propagating waves arrive first, the shorter slower propagating waves arrive last.

Group Speed (Deep water only): V=C/2.
Individual crests propagate at C.
Wave groups, packets or trains propagate at V.

7. Deepwater Wave Interactions

Waves can be added linearly.

For 2 waves of equal amplitude A,
If the crests intersect, the total amplitude is 2A.
If the troughs intersect, the total depression is 2A.
If the crest and trough intersect, they cancel.

Crossing Sea - 2 wave trains crossing at an angle - checkerboard pattern.

Rogue Waves - large episodic waves formed by the superposition of several wave crests and interactions with topography or strong currents. 20-30 m high.

8. Shallow Water Waves (Water Depth D < L/20):

Particle orbits go from circular to elliptical.

Wavelength: L = sqrt(gd)T

Phase speed now only depends on water depth: C = gD
Waves slow down as water depth decreases.

Shallow Water Waves are Nondispersive:
In the same water depth, waves with different periods now trael at the same speed.

Group speed now equals phase speed: V=C

9. Interactions with bottom topography and other features

Refraction: as a wave crest approaches a beach at an angle, the side in shallow water travels slower than the side in deep water.
The wave crest turns toward the beach.

Reflection: if a wave encounters a very steep beach or wall, it can be reflected.
Reflected waves can combine with the incoming progressive wave.

Diffraction: If part of a wave crest is blocked by an obstruction, wave energy is transported at right angles to the propagation direction into the undisturbed area behind the obstacle.
Waves propagating through a hole in a breakwater will spread out in semicircles in the undisturbed water beyond the breakwater.

10. Surf Zone

Region of wave breaking.

Plunging Breakers - steep beach - quick release of energy.
Spilling Breakers - wide beach - slow release of energy.

Breakers transport water shoreward. The transported water returns to the sea in narrow rip currents.

11. Tsunamis

Seismic sea waves - caused by earthquakes

Height 1-2 m
Wavelength 100-200 km
Period 10-20 min.

Ocean Depth - 4000 m, so Tsunamis are shallow water waves.

As tsunamis approach the shore, all the energy over the entire 4000 m depth of the ocean if compressed into a shallower region, so the amplitude increases to up to 30 m.

12. Storm Surge

Similar to Tsunamis but storm generated.

13. Internal waves

Similar to surface waves but occurring on a density difference interface within the ocean.

14. Standing waves.

Stationary waves due to the interference of a progressive wave with a perfectly reflected wave.

Seiches - sloshing of water that occurs in natural basins (harbors, lakes).

Antinode - areas that alternate between a crest and a trough.
Node - areas between antinodes where there is no change in elevation from the equilibrium surface.