Post on 20-Apr-2017
• 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)
Height (H) = crest to trough distance
Wavelength (L) = crest to crest distanceSteepness = H/L (waves break when H/L>1/7)
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
Wind-Driven Waves• Capillary Waves --> Gravity Waves (Chop) --> White Caps --> Swell
• Can be Deep or Shallow waves
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)
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
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
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!