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

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

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 betweenthe passage of successive crests Wave Height( H )vertical distance betweenany crest and succeeding trough Wavelength( L )horizontal distance betweensuccessive 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” http://www.gmi.edu/~drussell/Demos/waves/wavemotion.html

8. 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 Wave Equations

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 ( 100-200 meters ) • Periods of 10-20 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 http://hurricanes.noaa.gov/prepare/surge.htm

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