The interface between air and sea is almost always in motion

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Waves

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

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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

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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)

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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

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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

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Wave Period ( T ) time interval between the
passage of successive crests
Wave Height ( H ) vertical distance between any
crest and succeeding trough
Wavelength ( L ) horizontal distance between
successive crests or troughs
Celerity (Wave Speed) ( C ) C L / T (or
wavelength / period)
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Wave Motion

• Wave motion is oscillatory a sequence repeated
  with passage of each wave. Parcels move up and
  downnot forward.

The slinky does not move with the wavethe 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/wavemotio
n.html
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Wave Equations

• 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

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Relative wavelengths of different types of waves

• Capillary waves - lt 1.73 cm
• Wind Wave 60 150 m
• Seiche Large, variable a function of basin
  size
• Tsunami 200 km
• Tide ½ circumference of Earth

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Wave Generation by Wind

• Wind waves are gravity waves
• Begin as small capillary waves (lt1.73 cm)

Fine wrinkling of the surface
Restoring force is surface tension
Also known as Wavelets or ripples
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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

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Wind Waves breaking on shore
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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

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Swells at sea are hardly noticeablebut, as they
reach the shore of Hawaii they are!
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Wave Trains

• Wave trains can be followed from storm source to
  distance shoresoften ahead of the storm

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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

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• 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.

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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.

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Deep and Shallow Water Waves

• A deep water wave is when
• dgtL/2
• A shallow water wave is when
• dltL/20
• Intermediate waves are in-between dgtL/2 and
  dltL/20
• ddepth of water, Lwavelength

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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.

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• 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
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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)
• cgT/2p
• Simplified, c1.56T
• Thus, the longer the wavelength, the greater the
  celerity

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Period of a deep water wave

• L(g/2p)(T2)
• Since we know LcT we can substitute
• LgT2/2p or L1.56T2

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Waves in Shallow Water

• As waves move into shallow water (dltL/20) where
  d depth of water

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• Waves break when oversteepened and
• whitecaps are observed
• Observations through time suggest maximum wind
  waves with L at 800 meters, T23 s, c36 m/s
  suggest wave height to 36 meters!

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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 L156m can have a Height of 22 m!
• Highest observed winds West Wind Drift (strong
  winds, long fetch)

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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 wordstop half is a sinusoidal wave
• Path of particles are more elliptical
• All water in the wave moves in the direction of
  the wave

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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

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At the Shore

• The celerity of the base of a wave is c(gd)/2.
• Butthe crest moves faster than the base of the
  wave
• c(g(dH))/2
• Also, H0.75d
• Therefore, a 3 meter wave breaks in 4 meters of
  water depth

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Types of wave breaks

• Type of wave break depends on bottom
• Plunging waves from steeply sloping bottoms
• Spilling wave from gentle slopes

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Wave Power!

• Wave energy is proportional to the square of H.
• Energy/Unit Area1/8pgH2
• pdensity of water

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Longshore Currents

• Occur when hits shore at angle
• Water transported along beach until an exposed
  point reflects it seaward

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Rip Currents

• Occur where long shore currents flow out to sea
• Water moves rapidly, cutting channels in off
  shore sand bars
• Swimming hazard!

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Seismic Waves or Tsunamis

• Origin
• Sudden movement in Earths 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

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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

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Tsunamis

• As wave approaches the shore the speed is Cvgd
• Average speed is 200 m/s or 400 mph
• At sea, average height is only 0.5 m -gt hardly
  noticeable!!
• At shoreif trough arrives first, sea level
  dropsif crest, a rapidly forming high wave
  appears

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Tides

• Real tidal waves
• Largest wavelength ½ the circumference of Earth

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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

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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

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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

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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

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Internal Wave Packets
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Slicks

• Occur when sub surface internal wave crest breaks
  surface layer
• Most likely to occur in coastal areas where fresh
  water overlays salty water

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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

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Seiches

• Are standing waves
• Triggered by tectonic waves or storm surges
• Water oscillates by a period defined by the
  dimensions of the basin

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