Download the ocean

THE OCEAN
Supplement to GEO1030
Jan Erik H. Weber
Department of Geosciences, University of Oslo,
P. O. Box 1022, Blindern, N-0315 Oslo, Norway.
E-mail: [email protected]
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Preface
This note is a supplement to GEO1030 “Winds, Currents and Climate”. It has been difficult to
find a textbook that gives a short account of the fundamentals of physical oceanography that fits
into this course. Therefore, we have produced this small text with selected topics from the
ocean. An overview of the major currents of the world’s oceans is found in chapter 8 of the
textbook “Understanding Weather & Climate” by Aguado and Burt, which is used in the
meteorology part of this course, and will not be repeated here.
Blindern, Autumn 2005.
J. E. H. W.
Contents
1. Ocean basins
p. 3
2. Seawater composition
p. 5
3. Origin of salts in the ocean
p. 7
4. Salinity and density of seawater
p. 9
5. Sea ice formation
p. 11
6. Sound and light in the sea
p. 12
7. Distribution of temperature and salt
p. 14
8. Ocean waves
p. 17
9. Tsunamis
p. 20
•
General
•
The tsunami in the Indian Ocean December 26, 2004
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1. Ocean basins
The oceans cover 70.8 per cent of the earth's surface, and the mean ocean depth is about
3800 m. Nearly 1.4×109 km3 , or 97.2 per cent of the free water on earth, is stored in the ocean.
Typically, the ocean depth does not vary gradually over large horizontal distances. Instead, we
find a bottom topography with steep slopes and large, flat plains; see the sketch below.
Fig. 1 Principal features of the ocean floor bordering the continents.
The continental shelf extends seaward from the shore and has a typical depth of 100 200 m, and a gradient of about 1/500. The width of the continental shelf varies considerably in
various parts of the oceans. For example, in much of the Pacific it is not more than a few tens of
kilometers, while in the Arctic Sea we find the Siberian Shelf which in certain places is nearly
800 km wide. Shelf areas are very important since the waters here are rich in nutrients and
therefore rich in biologic activity. In fact, most of the world's fisheries occur on the shelves or in
shallow shelf seas like the North Sea or the Barents Sea.
At the shelf break, we find the start of the continental slope; see Fig. 1. The slope is
much steeper than the shelf. We here find average gradients of 1/20. This means that the
continental slopes are considerably steeper than the corresponding mountain slopes on land. The
continental slopes are very important for the oceanic circulation, since they tend to steer the
ocean currents along their depth contours, i.e. the iso-lines of constant depth. Sometimes we
find continental shelves and continental slopes cut by submarine canyons, especially near the
mouth of major rivers, e.g. the Congo Canyon. Some of the canyons are as large as the Grand
Canyon of the Colorado River. However, we also find canyons that have no obvious connection
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with large rivers. The transition between the continental slope and the deep sea is called the
continental rise.
The deep sea is characterized by abyssal plains, mid-ocean ridges, seamounts and ocean
trenches. In the deep sea, the abyssal plains dominate. Here we find large areas where the sea
floor is very smooth and very flat. Slopes as small as 1/50000 have been encountered in the
western North Atlantic. Mid-ocean ridges and ocean trenches; see Fig. 2, are results of the drift
of the continental plates.
Fig. 2 Features of the deep sea floor.
The mid-ocean ridges are formed when magma (molten rock) from the interior of the
earth is cooled in contact with the sea water and solidifies. Here new sea floor continuously
forms. The contact between the hot, basaltic rock at the mid-ocean ridges and the seawater helps
explain the chemical composition of seawater, as will be discussed later on. The most
prominent ridge is the Mid-Atlantic Ridge. It extends in the north-south direction and divides
the Atlantic Ocean into two parts. It may in places reach as much as 3 km above the ocean floor.
The total length of ocean ridges is about 60.000 km. However, the various ridges do not
everywhere constitute continuous obstructions for deep-water flow. There are narrow gaps or
fracture zones across the ridges that allow water to pass in certain places. A realistic picture of
the North Atlantic bathymetry is given in Fig. 3.
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Fig. 3 Bathymetric map of the North Atlantic. From Smith and Sandwell, 1997 (Smith, W.H.F. and D.T.
Sandwell, 1997. Global Seafloor topography from satellite altimetry and ship depth soundings. Science, 277,
1957 - 1962).
The ocean trenches are formed when one continental plate is bending down and sliding
beneath another. The ocean depth at the trenches can be more than 10 km. The majority of the
trenches are found in the Pacific, as the Philippine and the Mariana Trenches. The greatest depth
recorded in the ocean is 11.035 m, and is found in the Mariana Trench. Often island arcs, which
are bands of volcanic islands, are found parallel to the ocean trenches, e.g. the Aleutian Islands
outside Alaska. Seamounts are isolated, individual mountains of volcanic origin. They are
widely distributed in the oceans. If they reach to the surface, they form islands, like the Azores
in the Atlantic
2. Seawater composition
On average, 1 kg of seawater consists of 96.5 per cent pure water and 3.5 per cent
dissolved substances. Probably all known elements are dissolved in seawater, but the
concentrations of some of them are so small that they cannot be measured. The main elements
dissolved in seawater are chlorine (Cl), sodium (Na), sulphur (S) (through sulphate SO4),
magnesium (Mg), calcium (Ca) and potassium (K). The dissolving properties of water are
related to the asymmetric structure of the water molecule H2O. Here the two hydrogen atoms are
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not symmetrically distributed with respect to the oxygen atom, but form an angle of 105o; see
Fig. 4.
Fig. 4 Sketch of a water molecule.
Although the water molecule is neutral (negative and positive charges are equal), the
asymmetric structure causes it to behave like an electric dipole on an atomic scale. Such
molecules are called polar molecules. This property yields weak hydrogen bonds between
adjacent water molecules.
Due to the polar nature of the water molecule, the dissolved substances will not appear
as neutral atoms or molecules. Some of the constituents will have their electrons stripped to
form positive ions, e.g. sodium Na+ (10.76 g/l), magnesium Mg++ (1.29 g/l), calcium Ca++ (0.41
g/l) and potassium K+ (0.40 g/l), while others will gain extra electrons to form negative ions,
e.g. chlorine Cl- (19.35 g/l) and sulphate SO4-- (2.71 g/l). The numbers in the parentheses denote
total gram ions per liter of standard seawater. We note that sodium and chlorine dominate
among the positive and negative ions, respectively. When the water is removed by evaporation,
the elements combine to yield sodium chloride (table salt) NaCl (77.76%), magnesium chloride
MgCl2 (10.88%), magnesium sulphate MgSO4 (4.74%), calcium sulphate CaSO4 (3.60%) and
potassium sulphate K2SO4 (2.46%). The numbers here denote the percentage of total salts. We
see that the listed salts constitute more than 99 percent of all the salts in seawater.
Seawater also contains nitrogen, phosphate and silicate. These substances are nutrients
for phytoplankton (plant algae). The presence of nutrients in the surface layer of the ocean,
where there is sufficient light to support the growth and reproduction of plants (the so-called
euphotic zone), is a necessary condition for marine life. This is so because the production of
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phytoplankton in the euphotic zone is the main source of food for many larger marine
organisms.
At the sea surface there is an exchange of gases between the atmosphere and the ocean.
This means that the atmospheric gases can dissolve in water. The water is saturated with a
particular gas when the amount of gas dissolving in water is equal to the amount of gas leaving
the water at the same time. The total amount of gas that can be dissolved in seawater depends on
its temperature, salt content and pressure. Here, the temperature factor is the most important
one, and warm seawater can hold less gas than cold seawater. Stirring of the ocean surface layer
by wind and breaking waves facilitates the dissolution process, and the surface waters are
usually saturated with the atmospheric gases like oxygen and nitrogen. Normally, we find about
8 ml oxygen and 15 ml nitrogen per liter seawater in the saturation zone. In connection with
possible man-made climatic changes, there is a considerable interest related to the dissolution
and storage of carbon dioxide in the ocean. However, both oxygen and carbon dioxide in the
ocean are affected by chemical and biological processes that slowly, but continually change their
concentrations. In addition, a mass of water containing dissolved gases will exchange properties
with adjacent water masses through diffusion and turbulent mixing. Also, this water mass will
participate in the general circulation of the ocean (which is not particularly well known as far as
the deep sea is concerned).
3. Origin of salts in the ocean
Many of the components found in seawater come from weathering of rocks on land.
Rivers then bring these components to the sea. The idea that all salts in the sea are due to influx
from rivers goes back to the English astronomer Edmund Halley (1656-1742); the discoverer of
Halley's comet. Halley assumed that the ocean water originally was fresh, and that it gradually
became saltier by influx from the rivers. By measuring the yearly supply by all rivers and the
total amount of salt in the sea, Halley intended to calculate the age of the earth! However, there
cannot be any steady accumulation of salt in the ocean, as Halley thought. If that had been the
case, the oceans would long since have been saturated salt solutions like the waters of the Dead
Sea in Israel or the Great Salt Lake in the USA. In fact, a balance between the gain and the loss
of salt to the oceans must have been established long before the level of saturation was reached.
This balance is maintained through various chemical and biological reactions and bottom
depositions.
If the main source of salts in the ocean was river water, we would expect a large degree
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of similarity between the ionic composition of river water and seawater. In Fig. 5 (a, b) we have
depicted some of the constituents in the two types of water.
Fig. 5 Chemical composition of river water (a), and of seawater (b).
From these figures the differences are perhaps more striking than the similarities! It is a fact that
components like sodium (Na), calcium (Ca) and magnesium (Mg) in seawater may fully be
accounted for by the weathering of rocks and the subsequent transport by rivers. However,
surface rock material, and hence river water, contains far too little chloride (Cl) to account for
the abundance of this component in the ocean. To explain the relatively high concentrations of
chloride (and also sulphate) in seawater, we must take into account the steadily occurring
volcanic activity on earth. Eruptions on land and volcanic activity on the ocean floor release
gases that are rich in chloride and sulphate. Of particular importance here are the mid-ocean
ridges, where seawater comes into contact with hot, basaltic lava from the interior of the earth.
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The chemical processes that occur here are among the most important factors for controlling the
salt composition of ocean water.
4. Salinity and density of seawater
Before 1978 the salt content, or the salinity, was defined as the total grams of salt per
kilogram of seawater. Defined in this way, the salinity had no dimension, and it was expressed
in parts per mille (‰). Hence standard seawater with 35 grams of salt per kilogram of water had
a salinity of 35‰. Although the salinity varies from place to place in the ocean, it is a fact that
the ratio between the various salts is nearly constant! This result was established in the 1860s by
the Danish geologist Johan Forchhammer (1794-1865) from samples of surface water from
various parts of the world. The famous "Challenger" expedition 20 years later confirmed that
this was also the case for the deep-sea water. Utilizing that the ratio between the salts was
practically constant, one could measure the most abundant component in seawater, i.e. chloride,
and then calculate the content of the other salts. The following empirical formula has been used
to determine the salinity S:
S = 1.80655 Cl
(1)
where the chlorinity (in per mille) was determined by chemical analysis in the laboratory.
Since 1978 the salinity of seawater has been obtained by measuring the electrical
conductivity. Due to its ionic composition, seawater is a relatively good conductor of electricity.
The more ions (dissolved salts), the larger is the conductivity. This way of measuring the
salinity is more accurate, and much less time consuming, than the old method. From such
measurements it has become apparent that the ratio between the various salts is not exactly
constant, which means that (1) cannot be used to measure the salinity with sufficient accuracy.
For salinities determined by measuring the electrical conductivity, we use the unit psu (practical
salinity unit). Standard seawater then has a salinity S = 35 psu. The salinity varies in the ocean.
The variations are due to local differences between precipitation and evaporation, and even
more important, fresh water discharge from rivers. For example, in the Bothnian Bay in the
Baltic Sea, which has a large influx of river water, we find salinities as low as 5‰, while in hot
and dry areas with little runoff, like the Red Sea, the salinity of the surface water exceeds 40‰.
As far as physical oceanography is concerned, the main role of the dissolved salts is to
increase the density, i.e. the weight per unit volume, of seawater. For the density, it is only the
total amount of salt that is of importance, and we need not separate between the various salts.
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The density of seawater depends on temperature, salinity and pressure. These quantities are
related through the equation of state, which can be written
ρ = F (T, S, p)
(2)
The right-hand side of (2) turns out to be a long and complicated expression containing sums
and products of the various independent variables T, S and p, and we shall not write it explicitly
here (it nearly fills one printed page in a textbook). No surprise then, that oceanographers envy
the meteorologists that often can use the simple ideal gas equation ρ = p /(RT ) for the state of
the air, where R is a specific gas constant.
Pure water (S = 0) at atmospheric pressure has a maximum density when T = 4oC. This
is contrary to gases that always (at given pressure) become denser the colder they are. The
anomalous behavior of pure water is due to the weak bonds between the water molecules; see
Section 2. In fresh water lakes then, the surface water that cools during the autumn will be
denser at 4oC than the warmer (and therefore lighter) water below. Then thermal convection will
take place and surface water may reach the bottom of the lake. When the deeper parts of the lake
have reached a temperature of 4oC as a result of the convection process, further cooling will
make the surface water lighter, and convection will cease.
When salt is added, the maximum density of water (at given pressure) will be reached at
temperatures below 4oC. For seawater of salinity larger than 24.7 psu, the density increases
monotonically as the temperature decreases. In Fig. 6 we have displayed the density as function
of temperature for seawater of 35 psu.
Fig. 6 Density of seawater as function of temperature for S = 35 psu. The pressure is 1 bar.
As seen from Fig. 6, the density of seawater is close to 1000 kg/m3. In the open ocean the
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density may vary between 1020 and 1070 kg/m3, where the latter value corresponds to cold
water at very large depths.
5. Sea ice formation
Pure water at atmospheric pressure freezes at 0oC. When salt is added, the freezing point
is depressed. For seawater with salinity of 35 psu, the freezing point is close to -1.9oC; see Fig.
7.
Fig. 7 Freezing point Tf for seawater as function of salinity.
Standard seawater has a specific heat capacity of about 4.2 kJ/(kgoC). For comparison,
the corresponding specific heat capacities for dry air and rock material are about 1.0 and 0.8
kJ/(kgoC), respectively. The unusually high value for sea water is due to the bonds between the
water molecules, as discussed at the beginning of this section. The high heat capacity makes the
ocean capable of storing and transporting enormous amounts of energy. Since the heating of the
water is strongest near the equator, currents like the Gulf Stream that carry warm surface water
pole-ward, help to reduce the temperature differences between the tropics and the higher
latitudes.
When a mass of water freezes, a certain amount of heat is released. This is the same
amount of heat that must be applied to melt the ice in the reversed process. The energy flux
associated with the freezing/melting process is proportional to the latent heat of fusion, L. For
pure ice, L = 335 kJ/kg. When sea ice forms, the released energy is mainly used to heat the
atmosphere. The main part of the sea ice production occurs in the polar regions. However, the
ice does not stay permanently where it has been formed, but is drifting along under the influence
of winds and surface currents. For example, the ice produced in the Arctic Ocean stays there in
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average for about 3 years before it drifts out of the area. Most of it follows the East Greenland
Current and flows southward into the Greenland Sea as pack ice. Here melting takes place, but
some of the drifting ice may reach the north Atlantic before it finally melts. The heat needed for
the melting process is taken from the surrounding warm water, which in turn is cooled by that
process. In this way the formation of ice at high latitudes and the subsequent melting at lower
latitudes is equivalent to the pole-ward transport of warm surface water by ocean currents. They
both act to transfer energy pole-ward and thereby reducing the temperature differences between
equatorial and polar areas.
It is only pure water that freezes. Accordingly, when sea ice forms, the salt is rejected
back into the sea. However, some salt becomes trapped within the crystal structure of the ice
during the freezing process, where it forms so-called brine pockets. The degree of trapping
depends on the rate of freezing and the age of the ice. One year old sea ice has an average
salinity of about 4 psu. Through the process of salt rejection, the salinity of seawater may
increase considerably beneath a growing ice sheet. This salinity increase may render the surface
water more heavy than the water at larger depths, resulting in haline convection. It is believed
that this mechanism is important for the formation of intermediate and deep water in the Arctic
Ocean.
6. Sound and light in the sea
Sound is transmitted through a medium as a compression wave. We can define the
compressibility K of a fluid by
K=
1  dρ 


ρ  dp ad
(3)
where the subscript ad indicates that the considered change of state should be adiabatic, i.e.
with no exchange of heat (and salt) with the surroundings. The speed of sound Cs in a fluid is
related to its compressibility. It can be shown that
1/ 2
 1 

C s = 
 ρK 
(4)
The smaller the compressibility, the larger the speed of sound becomes. As can be judged from
the small range of densities found in the ocean, a parcel of seawater is not easily compressed. In
fact, a vertical water column of 10.000 m in the ocean is only about 200 m shorter due to
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compression than it would have been if the water was not compressible at all (K = 0)! Typically,
Cs is about 1.500 m/s in the ocean. Air is more compressible than water. In the atmosphere we
find that Cs is about 330 m/s.
The speed of sound in the ocean increases with increasing temperature, increasing
salinity and increasing pressure. This has an interesting consequence in open ocean areas where
the salinity varies little and warmer water is overlying colder water (which is in fact the case for
the major part of the world's oceans away from coasts and polar regions). In these areas Cs will
tend to increase with depth since the pressure increases with depth, but at the same time it will
tend to decrease with depth due to the temperature decrease as we move away from the surface.
In the upper part of the ocean the temperature effect will dominate, while deeper down the
pressure effect takes over. Consequently, the speed of sound will have a minimum at some
depth, typically around 1 km below the surface; see Fig. 8.
Fig. 8 Speed of sound Cs as function of depth in temperate areas of the oceans.
It is a well known fact that sound waves, especially at low frequencies, experience little
damping in the sea, i.e. ocean water is fairly transparent to low-frequency sound. Also,
according to the laws of wave propagation, a wave ray will always be deflected towards an area
of minimum wave speed. Accordingly, when sound is emitted from a location near the sound
minimum, the sound energy will not be spread everywhere, but will be trapped in a channel-type
region close to the minimum speed. This is often referred to as a sound, or SOFAR (Sound
Fixing And Ranging) channel. Here the sound may travel horizontally for thousands of
kilometers in the ocean; see Fig 9.
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Fig. 9 Trapped sound rays in a sound channel.
The existence of such sound channels is utilized by submarine vessels for
communication and surveillance. It is also speculated that whales may use these sound channels
to communicate over large distances.
We have seen that the ocean is quite transparent to low frequency sound waves. For
electromagnetic waves the situation is quite different. The earth receives solar radiation with
wavelengths in the range 0.3 to 3 µm. Depending on the conditions at the surface, 3 to 6 percent
of the incident radiation is reflected. When the sun stays low in the sky, the reflected fraction is
very much increased. About 50% of the radiation that strikes the sea surface is absorbed in the
upper meter of the ocean, while as much as 75% of this radiation is absorbed in the upper 10
meters. Most of this energy goes into heating the ocean water, while some is converted to
chemical energy through the process of photosynthesis.
In clear ocean water it is the blue part of the solar spectrum that penetrates to the largest
depth. In very clear water about 1% of the (incident 100%) blue light may reach a depth of 140
m. In coastal areas, where the water contains more dissolved and suspended material, the
penetration depth is dramatically reduced. Here it is the green light that penetrates to the largest
depth. Typically for the Oslo Fjord, we find 1% of the (incident 100%) green light at depths
around 5 m. The high degree of absorption of solar radiation by the ocean water explains why
biological activity that depends on photosynthesis can only occur in the surface layer.
7. Distribution of temperature and salt
Away from the polar regions, the absorption of solar energy in the top meters of the
ocean causes the temperature to be highest near the surface. Here wind and waves will act to
mix the water vertically so that the temperature becomes nearly constant with depth. This
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homogeneous surface layer is often called the mixed layer. The thickness varies with season and
latitude, ranging from 20 to 200 meters, say. Below the mixed layer the temperature decreases.
While the water in the mixed layer may have temperatures above 25oC in the tropics, we find
temperatures for the deep and bottom waters in these areas ranging from about 2 to 4oC. The
temperature variation with depth is strongest in the region just below the mixed layer. This
region is called the thermocline. In the open sea, away from polar and coastal areas, the density
of seawater is chiefly determined by its temperature. Therefore the density here will have its
strongest increase across the thermocline. This region of increase is called the pycnocline; see
Fig. 10.
Fig. 10 Temperature and density variation with depth for sub-polar, open ocean conditions.
In the interior of the ocean the salinity is fairly constant, having a value close to 35 psu.
At the surface it varies considerably; see Fig. 11, where we have sketched the average surface
salinity variation with latitude. In the same plot we have depicted the difference between
evaporation (E) and precipitation (P).
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Fig. 11 Average surface salinity (solid line) and excess of evaporation E over precipitation P (broken line) as
functions of latitude.
We note the clear correspondence between the maxima of surface salinity and E-P in the
relatively dry trade wind belts on both sides of the equator.
In bays and fjords, with fresh water supply from rivers, the stability of the water column
is often determined by the salinity distribution. Here we may have a relatively fresh layer above
saltier water. Again we may find a nearly homogeneous mixed layer on top. The largest salinity
variation occurs just below the mixed layer, where we find the halocline; see Fig. 12.
Fig. 12 Salinity distribution with depth in coastal areas.
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8. Ocean waves
The most commonly observed feature at the surface of the ocean is the presence of
ocean waves. In the ideal case a wave is a long sinusoidal disturbance that propagates along the
sea surface. The wave amplitude a is the distance from the mean surface level to the highest
point of the wave (the wave crest), and the wave height h is the vertical distance from the lowest
point of the wave (the wave through) to the wave crest, i.e. h = 2a. The wavelength λ is the
distance between to neighboring crests, and the mean ocean depth is H; see the definition sketch
in Fig. 13, where we have depicted a part of a wave at a given time (a photographic “snapshot”).
Fig. 13 Definition of wave parameters.
The wave motion is periodic in space, i.e. the surface elevation repeats itself after one
wavelength down the x-axis. Similarly, if we measure the position of the surface at one fixed
location (at a given x), it moves up and down periodically in time. The time that elapses from
we measure maximum surface elevation to the next maximum elevation occurs, is called the
wave period T. If we denote the surface elevation by the symbol η, we can write the surface
wave mathematically as
2π 
 2π
x−
t.
T 
 λ
η = a cos
Here a sinus-function would do equally well. We can also write (5) as
(5)
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 2π 
λ 
 x − t   = a cos(k ( x − ct )) ,
T 
 λ 
η = a cos
(6)
where we have defined the wave number k as k = 2π / λ , and the wave, or phase speed c as
c = λ / T . We realize that if we have a wave that propagates in a channel, and we bicycle along
the channel with speed c in the wave propagation direction, we will always follow the same
wave phase (a given wave crest, say). This explains why c = λ / T is called the phase speed.
The surface wave pattern moves with the wave speed c, but individual water particles
move with a much smaller velocity. If the wavelength λ is smaller than the ocean depth H, the
individual particles move approximately in circular orbits, where the radii decreases with depth,
see Fig.14.
Fig. 14 Motion of individual fluid particles due to surface waves propagating to the right. Solid dots denote particle
positions, and the straight arrows indicate horizontal water velocities at fixed mean levels.
The maximum velocity occurs at the surface. Here the radius of the particle motion is equal to
the wave amplitude a. Since a water particle makes a closed circular orbit in one wave period T,
its orbital velocity can be written vorb = 2π a / T . Hence we note that
vorb 2π a / T 2π
=
=
a = ka .
c
λ /T
λ
(7)
The last expression ka is called the wave steepness, and is always much smaller than 1 for
surface waves. Accordingly, the actual particle velocities associated with the wave motion is
much smaller than the phase speed of the wave.
Waves do transfer energy. The transfer of energy through a fixed vertical plane
perpendicular to the wave propagation direction is due to the work of the pressure. This can be
seen as follows: Consider the periodic pressure and the horizontal velocity at a certain water
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depth beneath the lowest surface level, at z = − L , say. Under wave crests the water velocity is
forwards, e.g. Fig. 14. Here the periodic pressure is positive because the water column above the
considered level is higher than the distance to the mean zero level, as indicated in Fig. 15a.
Under wave troughs the water velocity is negative. Here the periodic pressure is negative
because the water column above the considered level is shorter than the distance to the mean
zero level; see Fig. 15b.
Fig. 15 Periodic pressure and water velocity under a crest (a), and under a trough one half wave period later (b).
Accordingly, the product of the pressure times the velocity (the work per unit time) is always
positive, when averaged over one wave period. This work per unit time must equal the energy
propagation speed times the average wave energy. The energy propagation speed is often called
the group velocity. This is because the energy transfer in waves is related to groups of nearly
similar wave trains rather than one single sinus-wave.
When λ < H , the waves are called deep-water waves. In this case we find from wave
theory that the phase speed is given by c = ( gλ /( 2π ) ) , where g ( = 9.81 m/s 2 ) is the
1/ 2
acceleration due to gravity. We note that longer waves moves faster than shorter waves. Such
waves are generated by winds and storms in the open sea. In the generation area, a typical wave
period will be around 1 sec. Long, deep-water waves can move faster than the propagation of
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the storm center, and thus escape from the area. Such waves are called swell, and can propagate
for thousands of kilometers in the world’s oceans. A typical period for swell will be around 10
sec.
When λ >> H , we have shallow-water waves. In that case we find c = ( gH )1 / 2 . This
means that all shallow-water waves move with the same wave speed. In this case the particle
motion due to waves is mainly horizontal. When swell from distant storm areas hits the coasts,
where the water depth becomes smaller, these waves transform from deep-water waves to
shallow-water waves. Now the wave propagation is limited by the formula c = ( gH )1 / 2 .
Accordingly, faster propagating swell from behind caches up with the waves in front. This
means that the waves in the beach zone get shorter wavelengths and larger amplitudes. Finally
the waves will break. Breaking occurs because the wave crest moves faster than the rest of the
wave and makes the front steep. In certain areas the breaking will take the form of a plunging
breaker. The development towards a plunging breaker is sketched in Fig. 16.
Fig. 16 Sketch of plunging breaker.
9. Tsunamis
General
The word “tsunami” comes from Japanese and means “harbor wave”. This alludes to the
sudden damage such waves can do near the coast. Tsunamis are generated by sub-sea
earthquakes, volcanic eruptions or mud slides down continental slopes. The wave is set up by
the vertical displacement of large masses of water, and forms a local crest and/or trough at the
sea surface. This vertical displacement initiates a train of waves with crests and troughs that
propagates outward from the generation area. The typical wavelength of such a wave is
comparable to the dimensions of the area at the bottom where the vertical displacement took
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place. Such areas are usually several hundred kilometers in diameter. Therefore the tsunami is a
shallow-water wave. The amplitude in the open sea is small, typically one meter, or so.
Accordingly, in the open sea it is hardly noticeable to ship traffic. The waves propagate with the
shallow-water speed. With a mean ocean depth of 4000 m, the wave speed will be 720 km/h. In
shallower water, the wavelength will decrease and the wave amplitude will increase, because, as
explained before, the part of the wave in deeper water will move quicker than the wave front.
Depending of the steepness of the bottom slope, the wave may break. For islands with a very
steep continental slope, breaking may not occur, and the tsunami will be felt as relatively
harmless increase of the water level of a few meters. At less steep continental slopes, vigorous
breaking may occur. Then the tsunami front may appear as a vertical wall of water of several
tens of meters. How far inland the tsunami reaches, depends both of the wave height and of the
slope of the terrain.
The tsunami in the Indian Ocean December 26, 2004
This particular tsunami was generated by the faulting associated with a strong
earthquake (9 on the Richter magnitude scale) outside the north-west tip of Sumatra. The
direction of the fault was nearly north-south, with a length of about 1200 km and a width of
about 100 km. The maximum vertical bottom displacement was about 5 m upward in the west,
and about 2 m downward in the east, separated by a distance of about 50 km. The form of the
fault zone gave approximately a line source for the tsunami formation, with energy propagating
mainly in the east-west direction; see Fig. 17.
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Fig. 17 The 2004 Indian Ocean tsunami: Eastward and westward propagating waves after 10 min. Red: sea surface
elevation. Blue: sea surface depression (simulations by National Institute of Advanced Industrial Science and
Technology, Japan).
The area with initial downward fault motion in the east generated a surface wave that that
started out with a trough in the front, see Fig. 17. This trough propagated ahead of the first crest,
which explains why the water along the beaches in Thailand first retracted before the
subsequent breaking wave crest hit the shoreline. This did not happen in Sri Lanka, where the
wave crest hit the shore first. Fortunately, due to the orientation of the fault zone in the northsouth direction, relatively little wave energy went northwards. Therefore the densely populated
areas in low-land Bangla Desh were not particularly affected by the tsunami. In the open deep
ocean (here about 4000 m) the wave height was 1 – 2.5 m. The typical wavelength was about
100 km. In the shallow areas in West-Sumatra and West-Thailand wave heights of 10 - 15 m
were observed in the surf zone. The eastward tsunami hit Sumatra after about 5 min, while the
westward part of it reached Sri Lanka after about 2 hrs. A tsunami warning on Sri Lanka after
the unusually powerful earthquake in the ocean near Sumatra would have saved thousands of
lives, while the time was too short for a warning to have any effect in Sumatra. After Sri Lanka
the westward tsunami passed the low Maldivian Islands and caused great material damage.
Finally, after 6 – 8 hrs, the tsunami hit the east coast of Africa. Also here considerable damage
was inflicted, especially in Somalia. In total, more than 200.000 people were killed by this
tsunami.