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Wave  energy
Introduction  to wave energy
There   are   several   possibilities  to  harvest   different    forms   of  energy  from  the  sea.
One  of   these   options  is  the   usage   of  waves  for  the  generation  of  electricity.  The
devices  needed to  perform  this  task  are called wave energy  converters .
Wave energy is  indirect   solar  energy in twice. At  first  there is the wind, which is
caused by variations in atmospheric  pressure  due to a  differential  solar heating of
earth's surface by the sun. Different regions of pressure  drives  a  force  which  rises
movement  of atmospheric air masses that  causes  the earths wind system.
If  wind   strikes   over  the  surface  of  an   open   water,  waves  are  induced.  First  they
are very flat with only a low level of energy. When there is a long  distance  over
the  water  on  which  wind  can  attack  the  small  ones,  they   became   bigger  and
bigger with a lot of energy inside  them .
Physics  of wave energy
To have a better  understanding  of the technical possibilities to harvest the energy
out  of  waves  to   convert   it  into   electric   energy  it  may  be  helpful  to  have  a   look
onto  the  physics  of  wave   formation ,  the  forces  which  attack  and  the
characteristics  of water waves.
Wave formation
There are three different  momentum   responsible  for the formation of waves. The
moon , earthquakes and wind in variable intensities.
Energy of waves vs.  period  and responsible momentum
2
Three forces to attack the waves
There  are  three  forces  that  are  responsible  for  wave  formation.  Two  of  them
(gravitational force and  Coriolis  force) are supporting the formation, one of them
(surface tension) reduces the high of waves.
At first the gravitational force: This one out of  four  forces in physics is  dominant
for wave generation. The gravitational force drives the water from the crest of a
wave to wave  through . Because of this the potential energy of the elevated water
masses is converted into kinetic energy of the waves.
The coriolis force is a  minor  one. This force force is caused by the  rotation  of the
earth. Waves  which are caused by this force are very long. The wavelength  could
be about one km.
The  surface  tension   works   against  the  two  forces  mentioned   above .  The  force
caused by the tension of the surface is low and provokes more smaller waves.
From stresses to waves
Waves  caused  by  wind  are   build   over   deep    waters   and  energy-rich  waves  are
build  in  some  distance  from  the  equator.  If  air  is   moving   over  water  it  causes  a
tangential stress on the surface of the water. These stresses result in a formation
of waves.
The  turbulence  in  the  flow  of  the  air  creates  rapidly  varying  shear  stresses  and
pressure fluctuations. If the oscillations are ‘in phase’ with  already  existing waves
a furthermore in wave  development  occurs.
If waves have reached a certain high, wind can attack them directly and causes an
additional wave growth.
Wave  energy  is  a  very  dense  form  of  indirect  solar  energy.  To   compare   energy
densities:  mean  solar   power    density   on  earth  (over  a  year)  is  about  250 .
m2
Regarding waves this solar energy can be transferred up to 100 kW inside a wave
mcrl
per  meter  of crest  length .
3
Characteristics of waves
Due to the depth of the sea, the heaviness of the wind and the time that wind can
act the water surface, waves have different characteristics.
Characteristics of waves
Waves produced by a  strong  wind
Waves caused by a strong wind over a deep sea and for a long time
4
The  shape  of waves can be  described  by a sinusoidal form of a mathematical sine
function . The  following  values are  important  for a quantitative description of the
energy  stored  and the power of the waves:
Wave  high  h  is  the   difference    between   wave  crest  and  through.  The   higher   the
wave is, the more of energy is stored in it in form of potential energy.
@hD = m
The  wave  length  l  is  the  distance  between  two  wave  crests.  The  shorter  the
wavelength  the  more  of  energy  (potential)  can  be  transported  if  wave  high  and
velocity  stay  constant .
@lD = m
The  period  of  waves  is  the  time  between  two  following  wave  crests  over  a  fix
point over the  ground .
@tperD = s
The  frequency  f is the number of oscillating waves per second. It’s reciprocal is
the period.
= 1
D = 1
tper
s
The velocity v of a wave is defined as the  speed  over the ground. It is equal to the
wavelength divided by the period.
= l  
@vD = m
tper
s
The power of waves is  given  by
rH
=
O*g2* h2*tper
 
@PD = W
32 *p
mcrl
or  with  the  approximation   h2 ä tper.  The  power  is  defined  per  meter  of  crest
length.
ExerciseNorth  Atlantic  offshore  wave  conditions
Wave climate for the north Atlantic offshore region is given by the table  below .
The unknown values have to be calculated.
5
Period
High
Power density Velocity wavelength
@tD=s @hD=m
@PD= kW
@vD= m
@lD=m
m
s
calm
3.5
0.5
average
9
3.5
storm
14
14
Exercise: Power of waves
A wave climate is characterized by the following wave conditions: wave high is 1
m, the period is about 7  seconds .
Please  calculate the power of the waves per meter of crest length.
Exercise: Cycles of a wave collecting  device
A   typical   wave  climate  has  a  period  of   seven   seconds.  How  many  cycles  has  a
wave power  plant  to stay over lifetime of  twenty   years ?
6
Deep water waves
A parameter called relative water depth is used to distinguish the different zones
of wave- motion , which is the  ratio  of depth and wavelength.
relative water depht = dl
Water zones can be distinguished into:
- deep water:
> 1
l
2
intermediate  water:
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