oceanography seawaves chief mates june 2009

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Chief Mates….Notes prepared by Capt. Francis T. Gauci June2009

Oceanography: waves

theory and principles of waves, how they work and what causes them

When the wind blows across the water, it changes the water's surface,rst into ripples and then into waves. Once the surface becomes uneven,

the wind has an ever increasing grip on it. Storms can make enormouswaves, particularly if the wind, blows in the same direction for any lengthof time. In this chapter, you can learn what waves are and how theybehave. earn to understand the principles behind all surface waves.

1.Waves in the environment Without waves, the world would be a different place. Waves cannot exist by themselves for theyare caused by winds. Winds in turn are caused by differences in temperature on the planet,mainly between the hot tropics and the cold poles but also due to temperature fluctuations ofcontinents relative to the sea.Without waves, the winds would have only a very small grip on the water and would not be ableto move it as much. The waves allow the wind to transfer its energy to the water's surface and tomake it move. At the surface, waves promote the exchange of gases: carbon dioxide into theoceans and oxygen out. urrents and eddies mix the layers of water which would otherwise

become stagnant and less conducive to life. !utrients are thus circulated and re"used.The large ocean currents transport warm water from the tropics to the poles and cold water theother way. They help to stabilise the planet's temperature and to minimise its extremes. #orinstance, because of warm ocean currents arriving from the north, the temperature of !ew$ealand is %"& degrees higher than it would be without them.

#or the creatures in the sea, ocean currents allow their larvae to be dispersed and to be carriedgreat distances. any creatures spawn only during storms when large waves can mix theirgametes effectively.

oastal creatures living in shallow water experience the brunt of the waves directly. (n order tosurvive there, they need to be robust and adaptable. Thus waves maintain a gradient of

biodiversity all the way from the surface, down to depths of %)m or more. Without waves, therewould not be as many species living in the sea.

Waves pound rocks and make them erode faster, but sea organisms covering these rocks, delaythis process. Waves make beaches by transporting sand from deeper down towards the shore and

by washing the sand and removing fine particles. Waves stir and suspend the sand so thatcurrents or gravity can transport it.

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2.Wave motion Anyone having watched water waves rippling outward from the point where a stone was thrownin, should have noticed how effortlessly waves can propagate along the water's surface.Wherever we see water, we see its surface stirred by waves. (ndeed, witnessing a lake or sea flatlike a mirror, is rather unusual. *et, as familiar we are with waves, we are unfamiliar with how

water particles can +oin forces to make such waves.

Waves are oscillations in the water's surface. #or oscillations to exist and to propagate, like thevibrating of a guitar string or the standing waves in a flute, there must be a returning force that

brings e uilibrium. The tension in a string and the pressure of the air are such forces. Withoutthese, neither the string nor the flute could produce tones. The standing waves in musicalinstruments bounce their energy back and forth inside the string or the flute's cavity. Theoscillations that are passed to the air are different in that they travel in widening spheres outward.These travelling waves have a direction and speed in addition to their tone or timbre. (n air theirreturning force is the compression of the air molecules. (n surface waves, the returning force isgravity, the pull of the -arth. ence the name 'gravity waves' for water waves.

(n solids, the molecules are tightly connected together, which prevents them from moving freely, but they can vibrate. Water is a li uid and its molecules are allowed to move freely although theyare placed closely together. (n gases, the molecules are surrounded by vast expanses of vacuumspace, which allows them to move freely and at high speed. (n all these media, waves are

propagated by compression of the medium. owever, the surface waves between two media/water and air0, behave very different and solely under the influence of gravity, which is muchweaker than that of elastic compression, the method by which sound propagates.

The specific volume of sea water changes by only about & thousands of 1 percent /&-"20 under a pressure

change of one atmosphere /1 kg3cm 40. This may seem insignificant, but the 5acific 6cean would standabout 2)m higher, except for compression of the water by virtue of its own weight, or about 44cm higherin the absence of the atmosphere. 7ince an atmosphere is about e ual to a column of water 1)m high, theforce of gravity is about &% times weaker than that of elastic compression. 7urface tension /which forms droplets0 exerts a stress parallel to the surface, e uivalent to only one 8&millionth /1.&-"90 of an atmosphere. (ts restoring force depends on the curvature of the surface and isstill smaller. !evertheless it dominates the behaviour of small ripples /capillary waves0, whose presencegreatly contributes to the roughness /aerodynamic drag0 of the sea surface, and hence, to the efficiencywith which can generate larger waves and currents. (Van Dorn, 1974)

(f each water particle makes small oscillations around its spot, relative to its neighbours, wavescan form if all water particles move at the same time and in directions that add up to the wave's

shape and direction. ecause water has a vast number of molecules, the height of waves istheoretically unlimited. (n practice, surface waves can be sustained as high as 8); of the water'sdepth or some %)))m in a &)))m deep sea (Van Dorn, 1974).

!ote that the water particles do not travel but only their collective energy does< Waves that travelfar and fast, undulate slowly, re uiring the water particles to make slow oscillations, whichreduces friction and loss of energy.



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(n the diagram some familiar terms are shown. A floating ob+ectis observed to move in perfectcircles when waves oscillateharmoniously sinus"like in deep

water. (f that ob+ect hovered in thewater, like a water particle, itwould be moving alongdiminishing circles, when placeddeeper in the water. At a certaindepth, the ob+ect would stand still.This is the wave's base, preciselyhalf the wave's length. Thus longwaves /ocean swell0 extend muchdeeper down than short waves/chop0. Waves with 1)) metres between crests are common and could +ust stir the bottom down

to a depth of 2)m. !ote that the depth of a wave has little to do with its height< ut a wave'sheight contains the wave's energy, which is unrelated to the wave's length. =ong surface wavestravel faster and further than short ones. !ote also that the forward movement of the water undera crest in shallow water is faster than the backward movement under its trough. y thisdifference, sand is swept forward towards the beach.

Water waves can store or dissipate much energy. =ike other waves /alternating electric currents,e.g.0, a wave's energy is proportional to the s uare of its height /potential0. Thus a %m high wavehas %x%>? times more energy than a 1m high wave. When fine"weather waves of about 1mheight pound on the beach, they dissipate an average of 1)kW /ten one"bar heaters0 per metre of

beach or the power of a small car at full throttle, every five metres. / Ref Douglas L Inman in

Oceanography, he las fron ier, 1974 0. Attempts to harness the energy from waves have failed because they re uire large structures over large areas and these structures should be capable ofsurviving storm conditions with energies hundreds of times larger than they were designed tocapture.

Waves have a direction and speed. 7ound waves propagate by compressing the medium. Theycan travel in water about &.2 times faster than in air, about 12))m per second /2&))km3s, ormach"&.2, depending on temperature and salinity0. 7uch waves can travel in all directions andreach the bottom of the ocean /about &km0 in less than a second. 7urface waves, however, arelimited by the density of water and the pull of gravity. They can travel only along the surface andtheir wave lengths can at most be about twice the average depth of the ocean /4 x & km0. The

fastest surface waves observed, are those caused by tsunamis. The 'tidal wave' caused by anunder"sea earth uake in hile in ay 1?@), covered the @))) nautical miles /11,)))km0 to !ew$ealand in about 14 hours, travelling at a speed of about ?)) km3hr< When it arrived, it causedan oscillation in water level of ).@m at various places along the coast, 1.&m in Tauranga arbourand 4.&m in Whitianga harbour. !ote that tsunamis reach their minimum at about @))) kmdistance. eyond that, the curvature of the -arth bends the wave fronts to focus them again at adistance of about 14,))) km, where they can still cause considerable damage.

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3.Waves and wind

ow wind causes water to form

waves is easy to understandalthough many intricate detailsstill lack a satisfactory theory. 6na perfectly calm sea, the wind has

practically no grip. As it slidesover the water surface film, itmakes it move. As the water moves, it forms eddies and smallripples. (ronically, these ripples donot travel exactly in the directionof the wind but as two sets of

parallel ripples, at angles 8)"9)C tothe wind direction. The ripplesmake the water's surface rough,giving the wind a better grip. Theripples, starting at a minimum wave speed of ).4% m3s, grow to wavelets and start to travel in thedirection of the wind. At wind speeds of &"@ knots /8"11 km3hr0, these double wave fronts travelat about %)C from the wind. The surface still looks glassy overall but as the wind speed increases,the wavelets become high enough to interact with the air flow and the surface starts to lookrough. The wind becomes turbulent +ust above the surface and starts transferring energy to thewaves. 7trong winds are more turbulent and make waves more easily.

The rougher the water becomes, the easier it is for the wind to transfer its energy. The waves become steep and choppy. #urther away from the shore, the water's surface is not only stirred bythe wind but also by waves arriving with the wind. These waves influence the motion of thewater particles such that opposing movements gradually cancel out, whereas synchronisingmovements are enhanced. The waves start to become more rounded and harmonious. Dependingon duration and distance / fetch 0, the waves develop into a fully developed sea .

Anyone familiar with the sea, knows that waves never assume a uniform, harmonious shape.-ven when the wind has blown strictly from one direction only, the resulting water movement ismade up of various waves, each with a different speed and height. Although some waves aresmall, most waves have a certain height and sometimes a wave occurs which is much higher.

When trying to be more precise about waves,difficulties arise: how do wemeasure waves ob+ectivelyEWhen is a wave a wave andshould be countedE 7cientists

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do this by introducing a value E which is derived from the energy component of the compound wave. (nthe left part of the drawing is shown how the value E is derived entirely mathematically from the shapeof the wave. (nstruments can also measure it precisely and ob+ectively. The wave height is now

proportional to the s uare root of E . The sea state E is two times the average of the sum of the s uared amplitudes of all wave samples.The right part of the diagram illustrates the probability of waves exceeding a certain height. The verticalaxis gives height relative to the s uare root of the average energy state of the sea: h 3 7 B/ E 0 . #orunderstanding the graph, one can take the average wave height at 2); probability as reference. #ifty percent of all waves exceed the average wave height, and an e ual number are smaller. The highestone"tenth of all waves are twice as high as the average wave height /and four times more powerful0.Towards the left, the probability curve keeps rising off the scale: one in 2))) waves is three times higherand so on. The significant wave height % is twice the most probable height and occurs about 12; oronce in seven waves, hence the saying F-very seventh wave is highestF. lick here for a larger version of this diagram.

When the wind blowssufficiently long from thesame direction, the waves itcreates, reach maximum siGe,

speed and period beyond acertain distance /fetch0 fromthe shore. This is called afully developed sea . ecausethe waves travel at speedsclose to that of the wind, thewind is no longer able totransfer energy to them andthe sea state has reached itsmaximum. (n the picture thewave spectra of three differentfully developed seas areshown. The bell curve for a 4)

knot wind /green0 is flat andlow and has many high fre uency components /wave periods 1"1) seconds0. As the wind speedincreases, the wave spectrum grows rapidly while also expanding to the low fre uencies /to the right0.

!ote how the bell curve rapidly cuts off for long wave periods, to the right. ompare the siGe of the red bell, produced by &) knot winds, with that of the green bell, produced by winds of half that speed. Theenergy in the red bell is 1@ times larger<

mportant to remem!er is that the energy of the sea "ma#imum sea condition$ increases veryrapidly with wind speed, proportional to its fourth power. %he amplitude of the waves increases tothe third power of wind speed. %his property makes storms so une#pectedly destructive.

The biggest waves on the planet

are found where strong windsconsistently blow in a constantdirection. 7uch a place is foundsouth of the (ndian 6cean, atlatitudes of "&)C to "@)C, as shown

by the yellow and red colours onthis satellite map. Waves hereaverage 8m, with the occasional

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waves twice that height< Directly south of !ew $ealand, wave heights exceeding 2m are alsonormal. The lowest waves occur where wind speeds are lowest, around the e uator, particularlywhere the wind's fetch is limited by islands, indicated by the pink colour on this map. owever,in these places, the sea water warms up, causing the birth of tropical cyclones, typhoons orhurricanes, which may send large waves in all directions, particularly in the direction they are

travelling.

&.Waves entering shallow water

As waves enter shallow water,they slow down, grow taller andchange shape. At a depth of half its wave length, the roundedwaves start to rise and their crests

become shorter while their troughslengthen. Although their period/fre uency0 stays the same, thewaves slow down and their overallwave length shortens. The 'bumps'gradually steepen and finally

break in the surf when depth becomes less than 1.% times their height. !ote that waves changeshape in depths depending on their wave length , but break in shallows relating to their height <

ow high a wave will rise, depends on its wave length /period0 and the beach slope. (t has beenobserved that a swell of @"8m height in open sea, with a period of 41 seconds, rose to 1@m heightoff anihiki Atoll, ooks (slands, on 4 Hune, 1?@8. 7uch swell could have arisen from a @) knotstorm.

The photo shows waves entering shallow

water at 5iha, !ew $ealand. !otice how thewave crests rise from an almost invisible swellin the far distance. As they enter shallowwater, they also change shape and are nolonger sinus"like. Although their period remainthe same, their distance between crests andtheir speed, diminish.

!ot uite visible on this scale are the many

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surfies in the water near the centre of the picture. They favour this spot because as thewaves bend around the rocks, and gradually

break in a 'peeling' motion, they can ride themalmost all the way back to the beach.

Ioing back to the ' wave motion and depth ' diagram showing how water particles move, we cansee that all particles make a circular movement in the same direction. They move up on thewave's leading edge, forward on its crest, down on its trailing slope and backward on its trough.(n shallow water, the particles close to the bottom will be restricted in their up and downwardmovements and move along the bottom instead. As the diagram shows, the particle's amplitudeof movement does not decrease with depth. The forward3backward movement over the sandcreates ripples and disturbs it.

7ince shallow long waves have short crests and long troughs, the sand's forward movement ismuch more brisk than its backward movement, resulting in sand being dragged towards theshore. This is important for sandy beaches.

!ote that a sandy bottom is +ust another medium, potentially capable of guiding gravity waves. (t is about1.9 times denser than water and contains about %)"&); li uid. *et, neither does it behave like a li uid,nor entirely like a solid. (t resists downward and sideways movements but upward movements not asmuch. 7o waves cannot propagate over the sand's surface, like they do along the water's surface, butdivers can observe the sand '+umping up' on the leading edge of a wave crest passing overhead /when thewater particles move upward0. This may help explain why sand is so easily stirred up by waves and why

burrowing organisms are washed up so readily.

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7urf breakers are classified in three types:

• 'pilling !reakers: result from waves of low steepness /long period swell0 over gentleslopes. They cause rows of breakers, rolling towards the beach. 7uch breakers graduallytransport water towards the beach during groups of high waves. Bips running back to sea,transport this water a$ay from the beach during groups of low waves. When caught

swimming in a rip, do not attempt to swim back to shore because such rips can be verystrong /up to 9 km3hr0. 7wim parallel to the beach towards where the waves are highest.This is where water moves o$ar"s the beach. The next group of tall waves should assistyou to swim back to shore. owever, when launching /rescue0 boats, this is best done in arip Gone.

• (lunging !reakers: result from steeper waves over moderate slopes. The slope of a beach is not constant but may change with the tide. 7ome beaches are steep toward hightide, others toward low tide. A plunging breaker is dangerous for swimmers because itsintensity is greatly augmented by backwash from its predecessor. This strong backwash

precludes easy exit from the breaker Gone, particularly for divers. 6ften a steep bank ofloose sand prevents one from standing upright. (n order to exit safely, wait for a group of

low waves.• 'urging !reakers: occur where the beach slope exceeds wave steepness. The wave does

not really curl and break but runs up against the shore while producing foam and largesurges of water. 7uch places are dangerous for swimmers because the rapidly movingwater can drag swimmers over the rocks.

7pilling breakers are a familiar sighton most beaches. They arise fromlong waves breaking on gentlysloping beaches. There are several

5lunging breakers can occur onsteeply sloping beaches. There is onlyone row of breakers.

7urging breakers surge over steeplysloping /but not vertical0 beaches orrocks. Waves break one at a time.

%ho os Van Dorn, 1974



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rows of breakers.

When waves break, their energy is absorbed and converted to heat. The gentler the slope of the beach, the more energy is converted. 7teep slopes such as rocky shores do not break waves asmuch but reflect them back to sea, which 'shelters' marine life..

).Wave groups 5art of the irregularity of wavescan be explained by treating themas formed by interference betweentwo or more wave trains of different periods, moving in thesame direction. (t explains whywaves often occur in groups. Thediagram shows how two wavetrains /dots and thin line0 interfere,

producing a wave group of larger amplitude /thick line0. 7uch awave group moves at half theaverage speed of its componentwaves. The wave's energyspectrum, discussed earlier, doesnot move at the speed of thewaves but at the group speed.When distant storms send longwaves out over great distances,they arrive at a time thatcorresponds with the group speed,not the wave speed. Thus a groupof waves, with a period of 1&swould travel at a group velocity of 11m3s /not 44 m3s0 and take about4& hours /not 14 hr0 to reach theshore from a cyclone 1))) km distant. A group of waves with half the period /8s0 would taketwice as long, and would arrive a day later. (&arris, 19' )

ost wave systems at sea are comprised of not +ust two, but many component wave trains,having generally different amplitudes as well as periods. This does not alter the group concept,

but has the effect of making the groups /and the waves within them0 more irregular.

Anyone having observed waves arriving at a beach will have noticed that they are looselygrouped in periods of high waves, alternated by periods of low waves.

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oceanography seawaves chief mates june 2009

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