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The Waves
OCEA 101
• Why should you care?- waves provide as much
energy to the shore line as the sun
- near shore and breaking waves have a considerable influence on shoreline communities
Overview
• Wave characteristics• Wave motions• Deep water waves• Shallow water waves• Wave groups• Wave refraction, diffraction and reflection• Tsunamis• Standing waves
Waves• A wave is the transmission of
energy through a medium…this is true for all types of waves!
• The particles of the medium stay in the same general area (there are no “sound particles”)
Wave Types
• 3 Types of waves:– Transverse (side to side)– Longitudinal (up-down)– Orbital (circular movement)
For Simplicity, we will assume that ocean waves are Sine Waves (this isn’t actually true!)
• Net motion is up and down (bobbing)
• NOT a sine wave, so a slight forward motion as well
Mathematical Description
Height (H) = crest to trough distance
Height (H) = crest to trough distance
Wavelength (L) = crest to crest distance
Height (H) = crest to trough distance
Wavelength (L) = crest to crest distanceSteepness = H/L (waves break when H/L>1/7)
Period (T) = time for one wavelengthSpeed (C) = L/TFrequency (f) = 1/T, or C = L x f
Wave Classification
Wave Speed• Wave speed is given by:
- g= acceleration due to gravity = 9.81 m/s- tanh(x) is the hyperbolic tangent
• Deep water waves: d>L/2,
• Shallow water waves: d<L/20,
2 g 2 dC L tanh2 L
ππ
⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
22 d gtanh 1, C LL 2π
π⎛ ⎞ ⎛ ⎞≈ =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
22 d 2 dtanh , C gdL Lπ π⎛ ⎞ ≈ =⎜ ⎟
⎝ ⎠
Classification• Deep-Water Waves
Water depth (d) deeper than L/2C = L/T, but it’s hard to measure LC = gT / 2π, --> C = 156 x T (m/s)
Particles move in a circularpattern
Classification• Shallow-Water Waves (long waves)
Water depth (d) < 1/20 of LC = ( g x d )1/2 --> 3.1 x (d) 1/2
Therefore, as depth shallows, wave slows
Particles move elliptically, almost horizontally
Classification
• Transitional waves– Length is > 2x but less than 20x depth (d)– Properties are somewhere between deep-
water and shallow-water waves
Wave Relations
Wind-Driven Waves• Capillary Waves --> Gravity Waves (Chop) --> White Caps --> Swell
• Can be Deep or Shallow waves
Restoring Force: the source of energy dispersion that destroys a wave
Wind-Wave Formation
Waves increase energy by :
1) Wind Speed
2) Duration
3) Fetch
More Definitions…
• Sea: local waves formed by wind events• Confused Sea: local irregular waves of
many periods and from many directions• Fully developed Sea: the waves that
form when fetch, wind speed, and duration are maximal
• Wave Train: waves that have left the windy region and are sorted by period
Wave Trains• Sorted by
wavelength (and therefore speed)…this is wave dispersion
• These become swell
• Individual waves appear to be moving faster (2x) than the group velocity
Interference Patterns• All waves can be combined algebraically• They combine in 3 patterns:
– Constructive (phases match up)– Destructive (phases are exactly out of
alignment)– Mixed (most common…somewhere in
between)
Rogue Waves
Rogue Waves
• Can exceed 100 ft• “ship-killers”
Wave Trains
Storm Surge• Not really a wave
(we can’t apply our mathematical descriptions to it)
• Hurricanes “pile up” water in the right front quadrant
Tsunamis: “Harbor Wave”• Caused by a seismic
disturbance• Most common in the Pacific• Harmless until they hit the
coast
Internal Waves• Caused by changes in pycnocline• Doesn’t require much energy to get
them going
The Surf Zone…• Primary source of energy dissipation for
swell• When deep-water waves reach the
shore, they form breakers as H/L > 1/ 7
E=Total energy of a wave isdistributed over one wavelengthper unit width of crest from seasurface to depth of L/2.
E is proportional to H2
Recall that C=L/T
Shoaling waves or waves movingagainst a current slow downwhich means L decreases,meaning that H must increaseto conserve energy.
Hence shoaling waves increase inheight, steepen and eventually break.
Waves moving against a currentIncrease in height.
Refraction, Diffraction, Reflection
• Refraction: waves “feel bottom” and will turn (or get dragged) towards headlands
Refraction, Diffraction, Reflection
• Diffraction: waves can move around obstacles because energy is propagated in all directions
Wave Diffraction
Refraction, Diffraction, Reflection
Reflection: two waves of same wavelength, but moving in opposite directions, interact to form a standing wave. There is NO circular motion!
Seiches (Standing Waves)
Second Node Standing Waves