Waves

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Waves
The Horses of Neptune (Walter Crane, 1892)
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Waves everywhere in nature

• Sound waves,
• visible light waves,
• radio waves,
• microwaves,
• water waves,

• stadium waves,
• earthquake waves,
• waves on a string,
• slinky waves

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Waves

• Waves are energy moving through water
• Waves constantly pound the coast
• Most energy used to create currents transport
  sediment
• Modify the coasterode, deposit sediment
• Some energy reflected back to sea
• Need to have understanding of waves for coastal
  geology

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What is a wave?

• wave is disturbance traveling through a medium
  from one location to another.
• wave is the motion of a disturbance

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Classification of Waves

• According to distrubing force
• Gravity waves-periods of 1-30 seconds
• Generated by wind
• Restored by gravity

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Waves Origin and Type

• Wind waves wind-generated

• Seiche pressure-generated

• Tsunami seismic-generated

• Tide gravity-generated

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Wave Terminology

• Still water line level of ocean if it were flat
  w/o waves

• Crest highest part of wave
• Trough lowest part of wave

• Wave height (H) vertical distance between crest
  and trough

• Amplitude distance between crest and still
  water line

• ½ the wave height

• Wavelength (L) horizontal distance from each
  crest or each trough

• Or any point with the same successive point

• Steepness Height (H)/length (L)

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Wave frequency

• Frequency measures how often something happens
  over a certain amount of time.
• The number of waves that pass a particular point
  in a given time period

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Wave Period

• Period (T) the time it takes for two successive
  waves to pass a particular point. It also is the
  reciprocal of the frequency.
• T 1 / f
• f 1 / T

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Wave Speed

• What is the formula for velocity?
• velocity distance / time
• What distance do we know about a wave
• wavelength
• and what time do we know
• Period
• v ? / T
• but what does T equal
• T 1 / f
• so we can also write
• v f ?
• velocity frequency wavelength
• This is known as the wave equation.

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Deep Water Wave Motion

• Water particles move in orbits
• When under a wave crest
• Water moves up and forward
• When under a trough
• Water moves down and back
• Thus, water particles do not move forward
• They move in circles
• Particle motion ceases at ½ wavelength
• Diameter of orbits decrease with depth

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Waves Types

• Deep Water

• H2O depth is gt1/2 wavelength

• Shallow Water

• Depth is lt1/20 wavelength

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WavesVelocity

• Velocity (V) wavelength (L)/Period (T)

• For example

• If T 10 sec L 100 m

• Then 100 m/10 sec. 10 m/sec

• The longer the wavelength, the faster the wave
  travels

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Wave Formation
http//www.cc.ncu.edu.tw

• Wave formation transfer of energy from wind to
  waves.
• Ist surface is wrinkled
• Then wind enlarges waves
• Wind waves cannot grow infinitely large
• Limited by ratio of wave height to wave length
• Ratiosteepness
• Ratio will not exceed 1/7, when they reach limit
  they break

capillary wave,  small, free, surface-water wave
with such a short wavelength that its restoring
force is the waters surface tension, which
causes the wave to have a rounded crest and a
V-shaped trough. The maximum wavelength of a
capillary wave is 1.73 centimetres (0.68 inch)
longer waves are controlled by gravity and are
appropriately termed gravity waves. Unlike the
velocity of gravity waves, the velocity of
capillary waves increases with decreasing
wavelength, the minimum velocity being 23.1
centimetres per second (9.09 inches per second),
where the wavelength is the maximum 1.73 cm.
Britannica
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WavesGeneration

• Generated by Force

• wind or air

• Generated at storm centers

• Separation of waves by differing rates of travel
  - dispersion

• Sea Wrinkles ? ripples ? wind waves ? swells

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Wave Processes

• Wave dispersion
• Sea is storm area with mixture of wave periods
• These waves have differing velocities
• Waves with long period travel fastest
• Waves sort themselves
• This is known as wave dispersion
• The regular waves are called swell
• The longer the distance of transport from source,
  the greater the sorting of the waves become

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WavesSize

• Factors determining size

• Fetch

• Distance wind blows over open ocean

• Speed of wind

• Wind velocity

• Duration

• Length of time wind blows

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Waves Dispersion

• Wave train a set of waves with the same
  wavelength

• Individual waves move faster than wave train

• wave dies out at front of train while new waves
  form at rear

• Wave train travels half the speed of individual
  wave

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Swell
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Wave Interference

• Combination of waves

• Build from one another Constructive

• Cancel each other Destructive

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What can produce large waves

• Waves bending around an island
• Waves from different directions meeting
• These waves unpredictable

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Shallow Water Waves

• Swell feels bottom at depth lt ½ wavelength
• Velocity decreases as waves drag on floor
• Orbits progressively flatten at depth
• Wavelength decreases
• Wave height increases
• Wave breaks when H/L ratio gt 1/7
• Energy loss due to shoaling greater over wide low
  gradient shelfves
• In coastlines with steep fronts and narrow
  shelfs, energy loss due to bed friction are less

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Wave Shoaling

• What happens to waves when they enter intermdiate
  and shallow water depths
• Velocity decreases as waves drag on floor
• Wavelenght decreases
• Wave height increases
• Wave becomes unstable and breaks
• Energy loss due to shoaling greater over wide low
  gradient shelfves
• In coastlines with steep fronts and narrow
  shelfs, energy loss due to bed friction are less

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Breaking Waves

• Occurs when velocities of water particles at
  crest are greater than velocity of wave
• Wave breaks down into bubbles and foam
• Breaking waves release energy
• Releasing/dissapating energy can produce currents
  and move sediment

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Breaking wavesTypes

• Depends on steepness

• Type of Breakers

(a) Spilling

• Gentle slopes

• Surf gently rolls over the front

(b) Plunging

• Moderately steep slope

• Wave curls forming a tunnel

(c) Surging

• Steep slope

• Rolls onto beach

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Wave Refraction
www.crd.bc.ca

• Waves approach shore at an angle
• Wave part in deep water will move faster than
  wave part in shallow water
• The waves bend which is called wave refraction
• Waves tend to parallel the coast

www.crd.bc.ca
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Wave Breaking

• Occurs when velocities of water particles at
  crest are greater than velocity of wave
• Wave breaks down into bubbles and foam
• Breaking waves release energy
• Releasing/dissipating energy can produce currents
  and move sediment

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Types of waves

• Spilling
• Form on gently sloping beaches
• Gradually peaking of wave until it breaks
• Plunging
• Form on steeper beaches
• Form curling waves, best for surfing
• Surging Waves
• Form on steep beaches
• Crest and front of wave intact
• Move up beach

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WavesCharacteristics

• Diffraction
• Bending of waves around an obstacle like island,
  breakwater, reef
• Also bending of waves through small
  openingsAllows waves to enter narrow bays and
  harbor

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Wave Diffraction
esfscience.wordpress.com

• 1st image-opening small, but same as wavelength,
  get diffraction, waves do not slow down
• 2nd image-wider opening, greater than wavelength,
  only slight diffraction

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Wave Reflection

• Sometimes waves will not break but reflect at
  shoreline
• Occur at steep beaches and vertical shoreline
• Can form standing waves when reflected waves meet
  incoming waves

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Seiches

• Rise and fall of water level

• Occurs in enclosed basins and/or lakes

• Stationary point (node)

• Standing wave oscillates

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Tsunamis

• Giant sea waves generated by earthquakes

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TsunamiCauses

• Earthquake

• Volcanoes

• Landslides

• Meteor impact

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TsunamiCharacteristics

• Energy passes through entire water column

• Long periods (T)

• T 10-20 min.

• Small Height (H)

• H 1-2 m

• long wavelengths (L)

• L 100-200 km

• Shallow water wave

• Deep wave base

• Travel at great speeds

• c 200 m/s

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TsunamiCrest and Trough
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Historical Tsunamis1883 Krakatau

• Explosive volcano
• Large landmasses fell into the ocean
• 36,000 people killed by tsunami

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Historical Tsunamis1946 Pacific Tsunami

• Aleutian Island Earthquake
• Killed 165 people in Hawaii
• Resulted in the creation of the 1st tsunami
  warning system

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Historical Tsunamis2004 Indonesian Tsunami

• 9.0 M earthquake
• Deadliest tsunami ever recorded
• gt260,000 people killed

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Stop Here
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Anatomy of a Wave

• In our wave here the dashed line represents the
  equilibrium position.
• Once the medium is disturbed, it moves away from
  this position and then returns to it

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Anatomy of a Wave
crest

• The points A and F are called the CRESTS of the
  wave.
• This is the point where the wave exhibits the
  maximum amount of positive or upwards displacement

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Anatomy of a Wave
trough

• The points D and I are called the TROUGHS of the
  wave.
• These are the points where the wave exhibits its
  maximum negative or downward displacement.

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Anatomy of a Wave
Amplitude

• The distance between the dashed line and point A
  is called the Amplitude of the wave.\
• This is the maximum displacement that the wave
  moves away from its equilibrium.

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Anatomy of a Wave
wavelength

• The distance between two consecutive similar
  points (in this case two crests) is called the
  wavelength.
• This is the length of the wave pulse.
• Between what other points is can a wavelength be
  measured?

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Anatomy of a Wave

• What else can we determine?
• We know that things that repeat have a frequency
  and a period. How could we find a frequency and
  a period of a wave?

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Slinky Wave

• must first create a disturbance.
• must move a particle away from rest position.
• the disturbance continues down the slinky
• The pulse is transferred through the medium of
  the slinky, but the slinky itself does not
  actually move.
• So what really is being transferred? Energy!
• metal of slinky is MEDIUM that transfers the
  energy pulse of the wave.
• The medium ends up in the same place as it
  started it just gets disturbed and then returns
  to it rest position.
• The same can be seen with a stadium wave.

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Longitudinal Transverse Waves

• The differences between the two can be seen

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Wave Anatomy

• Assumes waves are regular
• Most waves irregular

Scripps CDIC
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Describing Irregular Waves

• Wave by wave analysis
• Identify individual waves in a record
• Calculate significant wave height of 1/3 of
  highest waves
• Good for coastal design purposes
• Root mean square wave height
• Square root of the mean squared wave height
• Rule of thumb Hs1.41 Hrms
• Mean wave period
• Mean period for all waves in record
• Significant wave period mean wave period of 1/3
  of highest waves in wave record

Scripps CDIC
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Spectral Analysis

• Produces wave spectrum
• Plot wave enegy vs frequency
• Graphs shows 2 wave fields
• Wave heights and periods in swell dominated
  coasts usually 1-2 m, 10 sec
• Wave hiehgts and periods for wind dominated
  coasts usually 0.5-1 m, 4 sec