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