1. The interface between air and sea is almost always in motion…
Waves
The interface between air and sea is almost always in motion…

2. What is a wave?
Waves represent a water surface displacement from still water level
Surface displacement is formed by a disturbing force (Example: Wind Stress)
Restoring force is Gravity
However, the wave continues because an upward force (buoyancy) exceeds the restoring force

3. Terms Crest – highest point of wave, portion above sea surface
Trough – lowest point of a wave, portion below sea surface
Wavelength – distance between any two equivalent points on successive waves (ex: distance between two crests)

4. Terms
Wave Height – The vertical distance between the top of the crest and bottom of the trough
Period – The time required for 2 successive crests or troughs to pass a point
Celerity – speed of the wave

5. Terms
Amplitude – distance wave moves water above or below sea level, equals ½ wave height
Frequency – number of waves passing a point in a given period of time
Propagation rate – number of waves passing a point in a given period of time

6. Wave Period ( T ) time interval between the passage of successive crests
Wave Height ( H ) vertical distance between any crest and succeeding trough
Wavelength ( L ) horizontal distance between successive crests or troughs
Celerity (Wave Speed) ( C ) C = L / T (or wavelength / period)

7. Wave Motion
Wave motion is oscillatory: a sequence repeated with passage of each wave. “Parcels” move up and down…not forward.
The slinky does not move with the wave…the wave displaces the slinky
Each “orbit” that a particle in
water experience with passage of
waves has diameter “H”

8. Wave Equations c = L / T T = L / c L = cT L = wavelength
SWL = still water level
n = water displacement from
H = wave height (distance from the crest to trough)
c = celerity (velocity)
T = wave period

9. Relative wavelengths of different types of waves
Capillary waves - < 1.73 cm
Wind Wave – 60 – 150 m
Seiche – Large, variable; a function of basin size
Tsunami – 200 km
Tide – ½ circumference of Earth

10. Wave Generation by Wind
Wind waves are gravity waves
Begin as small capillary waves (<1.73 cm)
Fine “wrinkling” of the surface
Restoring force is surface tension
Also known as Wavelets or ripples

11. Gravity or wind waves Formed when capillary waves overtake one another
Restoring force is gravity
Progressive groups of swell with the same origin and wavelength are called wave trains.
Occurs when wind is brisk – whitecaps
Periods between 1 and 30 seconds

12. Wind Waves breaking on shore

13. Swells
Waves that leave the fetch or generating area (could have left a storm at sea)
Have long periods and wavelengths, fast celerities
Energy transported a considerable distance
At sea, swells are hardly noticeable

14. Swells at sea are hardly noticeable…but, as they reach the shore of Hawaii they are!

15. Wave Trains
Wave trains can be followed from storm source to distance shores…often ahead of the storm

16. Main factors in development of wind waves
Wind strength
Wind duration (time that wind blows in one general direction)
Fetch (distance over which wind blows uninterrupted in one direction)
There is a maximum wave size for a combination of the 3 called a “fully developed sea”

17. Wind waves associated with storm winds mature into swells at a distance
Swells are more rounded and regular “sets” of waves
propagating at a distance from region of formation.
Regional sets or wavetrains form as groups of larger
waves
*Note: storm winds generally blow across areas of relatively small fetch for short periods. Fully developed seas rarely occur. Nonetheless, large storms are important wave generators.

18. Role of Water Depth in Wave Behavior
Water surface waves behave differently depending on the relationship between water depth and wavelength of the wave series.
Waves behave differently in “deep” and “shallow” water.

19. Deep and Shallow Water Waves
A deep water wave is when:
d>L/2
A shallow water wave is when:
d<L/20
Intermediate waves are in-between d>L/2 and d<L/20
d=depth of water, L=wavelength

20. Differences between deep-water and shallow water waves
The paths of water molecules in a wind wave are circular only when the wave is traveling in deep water, that is water that is deeper than one half of the waves length.
Once water depth is less than one half of the waves length, the circle becomes more and more elliptical.

21. Path of particle in a deep water wave is circular
Kinetic energy cuts a circular path
or ORBIT
b. Path of a particle in a shallow
water wave becomes more
elliptical as the wave moves
further into shore

22. Speed of a Deep Water Wave
The celerity of a deep water wave is independent of wave height and density of water (applies to salt or fresh water)
Can be expressed in terms of Period (T):
c=gT/2π
Simplified, c=1.56T
Thus, the longer the wavelength, the greater the celerity

23. Period of a deep water wave
L=(g/2π)(T2)
Since we know L=cT we can substitute
L=gT2/2π or L=1.56T2

24. Waves in Shallow Water
As waves move into shallow water (d<L/20) where d= depth of water

25. Waves break when oversteepened and
whitecaps are observed
Observations through time suggest maximum wind waves with L at 800 meters, T=23 s, c=36 m/s suggest wave height to 36 meters!

26. How Big is Big?
There is a limitation on height, such that the steepness of a wave lank does not usually exceed about 60° vertically.
Rule of Thumb: 1/7 ratio of H/L
Ex: A wave with L=156m can have a Height of 22 m!
Highest observed winds: West Wind Drift (strong winds, long fetch)

27. Characteristics of shallow water waves as they “feel” the bottom
Crest becomes more peaked
Trough becomes more flattened
Wave resembles a “solitary” wave
where H (wave height) is above SWL
in other words…top half is a sinusoidal wave
Path of particles are more elliptical
All water in the wave moves in the direction of the wave

28. Celerity of Shallow Water Waves
Related only to water depth (not wavelength or period as in deep-water waves)
c=(gd)/2
Thus, waves move slower in shallow water

29. At the Shore The celerity of the base of a wave is c=(gd)/2.
But…the crest moves faster than the base of the wave:
c=(g(d+H))/2
Also, H=0.75d
Therefore, a 3 meter wave breaks in 4 meters of water depth

30. Types of wave breaks Type of wave break depends on bottom
Plunging waves from steeply sloping bottoms
Spilling wave from gentle slopes

31. Wave Power! Wave energy is proportional to the square of H.
Energy/Unit Area=1/8pgH^2
p=density of water

32. Longshore Currents Occur when hits shore at angle
Water transported along beach until an exposed point reflects it seaward

33. Rip Currents Occur where long shore currents flow out to sea
Water moves rapidly, cutting channels in off shore sand bars
Swimming hazard!

34. Seismic Waves or Tsunamis
Origin:
Sudden movement in Earth’s crust causes rise in sea level
Under water volcanoes/earthquakes
Characteristics
Long periods of 1-2 hours
Waves exceed 30 meters
on shore
Wave speed can
equal 400 mph

35. Tsunamis Properties Water rushes to the central point of disturbance
Waves of long wavelength ( meters )
Periods of minutes
Ocean depth in excess of 400 meters, thus does not affect depth of the wave

36. Tsunamis As wave approaches the shore the speed is C=√gd
Average speed is 200 m/s or 400 mph
At sea, average height is only 0.5 m -> hardly noticeable!!
At shore…if trough arrives first, sea level drops…if crest, a rapidly forming high wave appears

40. Tides Real “tidal waves”
Largest wavelength ½ the circumference of Earth

41. Storm Surge Form during periods of excessively high water
Caused by changes in atmospheric pressure and wind
When combined with high tide, can produce disaster on coastal regions

42. Causes of storm surge
Major storms: under a low pressure system, the sea will rise to dome or hill of water
As the storm approaches, the dome of water approaches

43. Internal Waves: Surface
Occur at a boundary between air and water
Occur because fluids are of different density
Therefore, surface waves will form along a boundary between two fluids of different density

44. Internal Waves: beneath surface
Although differences are small, waves form along boundary of any to fluids of different density (differences between salinity or temperature)
Waves are large in amplitude and slow in speed

45. Internal Wave Packets

46. Slicks Occur when sub surface internal wave crest breaks surface layer
Most likely to occur in coastal areas where fresh water overlays salty water

47. Standing Waves Non-progressing
Crests appear to alternate about a fixed point called a node
End points of wave called antinodes
Properties: the period of oscillation can increase if:
Either the length of the basin increases
The depth of the water decreases

48. Seiches Are standing waves Triggered by tectonic waves or storm surges
Water oscillates by a period defined by the dimensions of the basin