The interface between The interface between air and sea is almost air and sea is almost

always in motion…always in motion…

Waves

What is a wave?What is a wave?

Waves represent a water surface Waves represent a water surface displacement from still water leveldisplacement from still water level

Surface displacement is formed by a Surface displacement is formed by a disturbing force (Example: Wind disturbing force (Example: Wind Stress)Stress)

Restoring force is GravityRestoring force is Gravity However, the wave continues because However, the wave continues because an upward force (buoyancy) exceeds an upward force (buoyancy) exceeds the restoring forcethe restoring force

TermsTerms

Crest – highest point of wave, Crest – highest point of wave, portion above sea surfaceportion above sea surface

Trough – lowest point of a Trough – lowest point of a wave, portion below sea surfacewave, portion below sea surface

Wavelength – distance between Wavelength – distance between any two equivalent points on any two equivalent points on successive waves (ex: distance successive waves (ex: distance between two crests)between two crests)

TermsTerms

Wave Height – The vertical Wave Height – The vertical distance between the top of the distance between the top of the crest and bottom of the troughcrest and bottom of the trough

Period – The time required for Period – The time required for 2 successive crests or troughs 2 successive crests or troughs to pass a pointto pass a point

Celerity – speed of the waveCelerity – speed of the wave

TermsTerms

Amplitude – distance wave moves Amplitude – distance wave moves water above or below sea level, water above or below sea level, equals ½ wave heightequals ½ wave height

Frequency – number of waves Frequency – number of waves passing a point in a given period passing a point in a given period of timeof time

Propagation rate – number of waves Propagation rate – number of waves passing a point in a given period passing a point in a given period of timeof time

Wave Height ( H ) vertical distance between any crest and succeeding trough

Wavelength ( L ) horizontal distance between successive crests or troughs

Wave Period ( T ) time interval between the passage of successive crests

Celerity (Wave Speed) ( C ) C = L / T (or wavelength / period)

Wave MotionWave Motion Wave motion is oscillatory: a Wave motion is oscillatory: a sequence repeated with passage of sequence repeated with passage of each wave. “Parcels” move up and each wave. “Parcels” move up and down…not forward.down…not forward.

The slinky does not move with the wave…the wave displaces the slinky

Each “orbit” that a particle inwater experience with passage ofwaves has diameter “H”

http://www.gmi.edu/~drussell/Demos/waves/wavemotion.html

Wave EquationsWave Equations

c = L / Tc = L / T T = L / cT = L / c L = cTL = cT

L = wavelengthL = wavelength

SWL = still water SWL = still water levellevel

n = water n = water displacement from displacement from

H = wave height H = wave height (distance from the (distance from the crest to trough)crest to trough)

c = celerity c = celerity (velocity)(velocity)

T = wave periodT = wave period

Relative wavelengths of Relative wavelengths of different types of wavesdifferent types of waves

Capillary waves - < 1.73 cmCapillary waves - < 1.73 cm Wind Wave – 60 – 150 mWind Wave – 60 – 150 m Seiche – Large, variable; a Seiche – Large, variable; a function of basin sizefunction of basin size

Tsunami – 200 kmTsunami – 200 km Tide – ½ circumference of EarthTide – ½ circumference of Earth

Wave Generation by WindWave Generation by Wind

Wind waves are gravity wavesWind waves are gravity waves Begin as small capillary waves Begin as small capillary waves (<1.73 cm)(<1.73 cm)

Fine “wrinkling” of the surface

Restoring force is surface tension

Also known as Wavelets or ripples

Gravity or wind wavesGravity or wind waves

Formed when capillary waves overtake Formed when capillary waves overtake one anotherone another

Restoring force is gravityRestoring force is gravity Progressive groups of swell with the Progressive groups of swell with the same origin and wavelength are same origin and wavelength are called wave trains.called wave trains.

Occurs when wind is brisk – Occurs when wind is brisk – whitecapswhitecaps

Periods between 1 and 30 secondsPeriods between 1 and 30 seconds

Wind Waves breaking on shore

SwellsSwells

Waves that leave the fetch or Waves that leave the fetch or generating area (could have left a generating area (could have left a storm at sea)storm at sea)

Have long periods and wavelengths, Have long periods and wavelengths, fast celeritiesfast celerities

Energy transported a considerable Energy transported a considerable distancedistance

At sea, swells are hardly At sea, swells are hardly noticeablenoticeable

Swells at sea are hardly noticeable…but, as they reach the shore of Hawaii they are!

Wave TrainsWave Trains

Wave trains can be followed Wave trains can be followed from storm source to distance from storm source to distance shores…often ahead of the stormshores…often ahead of the storm

Main factors in Main factors in development of wind wavesdevelopment of wind waves

1.1. Wind strengthWind strength2.2. Wind duration (time that wind Wind duration (time that wind

blows in one general direction)blows in one general direction)3.3. Fetch (distance over which wind Fetch (distance over which wind

blows uninterrupted in one blows uninterrupted in one direction)direction)

There is a maximum wave size for There is a maximum wave size for a combination of the 3 called a a combination of the 3 called a “fully developed sea”“fully developed sea”

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.

Role of Water Depth in Role of Water Depth in Wave BehaviorWave Behavior

Water surface waves behave Water surface waves behave differently depending on the differently depending on the relationship between water depth relationship between water depth and wavelength of the wave and wavelength of the wave series.series.

Waves behave differently in Waves behave differently in “deep” and “shallow” water.“deep” and “shallow” water.

Deep and Shallow Water Deep and Shallow Water WavesWaves

A deep water wave is when:A deep water wave is when:

d>L/2d>L/2 A shallow water wave is when:A shallow water wave is when:

d<L/20 d<L/20 Intermediate waves are in-between Intermediate waves are in-between d>L/2 and d<L/20d>L/2 and d<L/20

d=depth of water, L=wavelength d=depth of water, L=wavelength

Differences between deep-Differences between deep-water and shallow water waveswater and shallow water waves

The paths of water molecules in a The paths of water molecules in a wind wave are circular only when wind wave are circular only when the wave is traveling in deep the wave is traveling in deep water, that is water that is deeper water, that is water that is deeper than one half of the waves length. than one half of the waves length.

Once water depth is less than one Once water depth is less than one half of the waves length, the half of the waves length, the circle becomes more and more circle becomes more and more elliptical.elliptical.

a.Path of particle in a deep water wave is circular

b. Path of a particle in a shallow water wave becomes more elliptical as the wave moves further into shore

Kinetic energy cuts a circular pathor ORBIT

Speed of a Deep Water WaveSpeed of a Deep Water Wave

The celerity of a deep water wave is The celerity of a deep water wave is independent of wave height and independent of wave height and density of water (applies to salt or density of water (applies to salt or fresh water)fresh water)

Can be expressed in terms of Period Can be expressed in terms of Period (T):(T):

c=gT/2πc=gT/2π Simplified, c=1.56TSimplified, c=1.56T Thus, the longer the wavelength, the Thus, the longer the wavelength, the greater the celeritygreater the celerity

Period of a deep water Period of a deep water wavewave

L=(g/2L=(g/2π)(Tπ)(T22))

Since we know L=cT we can Since we know L=cT we can substitutesubstitute

L=gTL=gT22/2π or L=1.56T/2π or L=1.56T22

Waves in Shallow WaterWaves in Shallow Water

As waves move into shallow As waves move into shallow water (d<L/20) where d= depth water (d<L/20) where d= depth of waterof water

Waves break when oversteepened Waves break when oversteepened and and whitecaps are observedwhitecaps are observedObservations through time Observations through time suggest maximum wind waves with suggest maximum wind waves with L at 800 meters, T=23 s, c=36 L at 800 meters, T=23 s, c=36 m/s suggest wave height to 36 m/s suggest wave height to 36 meters!meters!

How Big is Big?How Big is Big?

There is a limitation on height, There is a limitation on height, such that the steepness of a wave such that the steepness of a wave lank does not usually exceed lank does not usually exceed about 60° vertically.about 60° vertically.

Rule of Thumb: 1/7 ratio of H/LRule of Thumb: 1/7 ratio of H/L Ex: A wave with L=156m can have a Ex: A wave with L=156m can have a Height of 22 m!Height of 22 m!

Highest observed winds: West Wind Highest observed winds: West Wind Drift (strong winds, long fetch)Drift (strong winds, long fetch)

Characteristics of shallow Characteristics of shallow water waves as they “feel” water waves as they “feel”

the bottomthe bottom Crest becomes more peakedCrest becomes more peaked Trough becomes more flattenedTrough becomes more flattened Wave resembles a “solitary” waveWave resembles a “solitary” wave

where H (wave height) is above where H (wave height) is above SWLSWL

in other words…top half is a in other words…top half is a sinusoidal sinusoidal wavewave

Path of particles are more ellipticalPath of particles are more elliptical All water in the wave moves in the All water in the wave moves in the direction of the wavedirection of the wave

Celerity of Shallow Water Celerity of Shallow Water WavesWaves

Related only to water depth (not Related only to water depth (not wavelength or period as in deep-wavelength or period as in deep-water waves)water waves)

c=(gd)/2c=(gd)/2

Thus, waves move slower in Thus, waves move slower in shallow watershallow water

At the ShoreAt the Shore

The celerity of the base of a The celerity of the base of a wave is c=(gd)/2. wave is c=(gd)/2.

But…the crest moves faster than But…the crest moves faster than the base of the wave:the base of the wave:

c=(g(d+H))/2c=(g(d+H))/2 Also, H=0.75dAlso, H=0.75d Therefore, a 3 meter wave breaks Therefore, a 3 meter wave breaks in 4 meters of water depthin 4 meters of water depth

Types of wave breaksTypes of wave breaks

Type of wave break depends on Type of wave break depends on bottom bottom

Plunging waves from steeply Plunging waves from steeply sloping bottoms sloping bottoms

Spilling wave from gentle Spilling wave from gentle slopes slopes

Wave Power!Wave Power!

Wave energy is proportional to Wave energy is proportional to the square of H.the square of H.

Energy/Unit Area=1/8pgH^2Energy/Unit Area=1/8pgH^2

p=density of waterp=density of water

Longshore CurrentsLongshore Currents

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

Rip CurrentsRip Currents

Occur where long shore currents Occur where long shore currents flow out to seaflow out to sea

Water moves rapidly, cutting Water moves rapidly, cutting channels in off shore sand barschannels in off shore sand bars

Swimming hazard!Swimming hazard!

Seismic Waves or Seismic Waves or TsunamisTsunamis

Origin: Origin: Sudden movement in Earth’s crust Sudden movement in Earth’s crust causes rise in sea levelcauses rise in sea level

Under water volcanoes/earthquakesUnder water volcanoes/earthquakes CharacteristicsCharacteristics

Long periods of 1-2 hoursLong periods of 1-2 hours Waves exceed 30 meters Waves exceed 30 meters on shoreon shore Wave speed can Wave speed can equal 400 mphequal 400 mph

TsunamisTsunamis

PropertiesProperties Water rushes to the central point Water rushes to the central point of disturbanceof disturbance

Waves of long wavelength ( 100-200 Waves of long wavelength ( 100-200 meters )meters )

Periods of 10-20 minutesPeriods of 10-20 minutes Ocean depth in excess of 400 Ocean depth in excess of 400 meters, thus does not affect depth meters, thus does not affect depth of the waveof the wave

TsunamisTsunamis

As wave approaches the shore the As wave approaches the shore the speed is C=√gdspeed is C=√gd

Average speed is 200 m/s or 400 Average speed is 200 m/s or 400 mphmph

At sea, average height is only At sea, average height is only 0.5 m -> hardly noticeable!!0.5 m -> hardly noticeable!!

At shore…if trough arrives first, At shore…if trough arrives first, sea level drops…if crest, a sea level drops…if crest, a rapidly forming high wave appearsrapidly forming high wave appears

TidesTides

Real “tidal waves”Real “tidal waves” Largest wavelength ½ the Largest wavelength ½ the circumference of Earthcircumference of Earth

Storm SurgeStorm Surge

Form during periods of Form during periods of excessively high waterexcessively high water

Caused by changes in atmospheric Caused by changes in atmospheric pressure and windpressure and wind

When combined with high tide, When combined with high tide, can produce disaster on coastal can produce disaster on coastal regionsregions

http://hurricanes.noaa.gov/prepare/surhttp://hurricanes.noaa.gov/prepare/surge.htmge.htm

Causes of storm surgeCauses of storm surge

Major storms: under a low Major storms: under a low pressure system, the sea will pressure system, the sea will rise to dome or hill of waterrise to dome or hill of water

As the storm approaches, the As the storm approaches, the dome of water approachesdome of water approaches

Internal Waves: SurfaceInternal Waves: Surface

Occur at a boundary between air Occur at a boundary between air and waterand water

Occur because fluids are of Occur because fluids are of different densitydifferent density

Therefore, surface waves will Therefore, surface waves will form along a boundary between form along a boundary between two fluids of different densitytwo fluids of different density

Internal Waves: beneath Internal Waves: beneath surfacesurface

Although differences are small, Although differences are small, waves form along boundary of waves form along boundary of any to fluids of different any to fluids of different density (differences between density (differences between salinity or temperature)salinity or temperature)

Waves are large in amplitude Waves are large in amplitude and slow in speedand slow in speed

Internal Wave Packets

SlicksSlicks

Occur when sub surface internal Occur when sub surface internal wave crest breaks surface layerwave crest breaks surface layer

Most likely to occur in coastal Most likely to occur in coastal areas where fresh water areas where fresh water overlays salty wateroverlays salty water

Standing WavesStanding Waves

Non-progressingNon-progressing Crests appear to alternate about a Crests appear to alternate about a fixed point called a nodefixed point called a node

End points of wave called antinodesEnd points of wave called antinodes Properties: the period of Properties: the period of oscillation can increase if:oscillation can increase if: Either the length of the basin Either the length of the basin increasesincreases

The depth of the water decreasesThe depth of the water decreases

SeichesSeiches

Are standing wavesAre standing waves Triggered by tectonic waves or Triggered by tectonic waves or storm surgesstorm surges

Water oscillates by a period Water oscillates by a period defined by the dimensions of defined by the dimensions of the basinthe basin