WATER WAVE
DYNAMICS AND THE
SECRET OF THE
TSUNAMIS
Presenters:
-Isaac Katz
-Zsuzsanna Kis
-Kinneret Rozales
Mentor: Ronen Avni
Location: Haifa, Technion city, Faculty Of Civil Engineering.
THE PHYSICS OF WAVES
The following mathematical equation, commonly referred to
as the wave equation served as the scientific foundation for this work.
Its derivatives are also here shown, although for shortness of space
not explained.
These basic equations have uncovered the firsts steps towards
an understanding of fluid dynamics in general and water-wave
behavior in particular and I think them crucial for any one to know
who has an interest in this subject
especially as they don’t require advanced education to understand.
WATER-WAVE EQUATION AND ITS
DERIVATIVES
ftt  v 2 fxx  0
z  x  vt
f 1  f ( x  vt)
f 2  f ( x  vt)
d df
( )
dt dt
d df
fxx 
( )
dx dx
df
g
* ( v )
dz
df
f
 g  f  * ( v )
dz
d df
d
dz
d2 f
d2 f
ftt  [ * ( v] 
[ f  * (v)] *
 v * 2 * (v)  v 2 * 2  v 2 fzz
dt dz
dz
dt
dz
dz
2
d df
d
dz
d f
d2 f
fxx 
[ * ( v ] 
[ f  * ( v)] *
 v * 2 * (v)  v 2 * 2  v 2 fzz
dx dz
dz
dx
dz
dz
ftt 
WAVE SPEED EQUATION
Long waves are non-dispersive: Their wave speed is independent of their period.
It depends only on the water depth, in the form:
( c is wave speed, h water depth, g gravity).
The velocity structure in a long wave is described by
where z is the time dependent surface elevation (wave amplitude)
and u the horizontal particle velocity. It follows that u is independent
of depth and the vertical particle velocity varies linearly with depth.
Particles move on very flat elliptic paths in nearly horizontal motion.
WAVES IN THE LAB
We can see examples of waves all around us,
Here we experiment with many objects to find out their properties
And see how they relate to waves.
Using a pendulum, a moving board
and some sand we can see the
interesting results that show us how
the same underlying sinus wave shape
forms on different situations and materials.
And here we can see a wave forming from the
rhythmical up and down movement of a spring rope.
The faster the rope is moved the more waves are formed,
with nodes and anti-nodes developing harmoniously with the movement,
we can thus see the rope evolving from a single waveform into multiple,
complicated patterns which are not always symmetric.
A demonstration of waves with normal
conditions approaching a ‘shore’
if looked at closely one can
distinguish de similarities of the basic
wave form with the picture in the right.
WHAT DOES TSUNAMI MEAN?
• Japanese word which in English means Harbor
•
•
Wave
Commonly known as ‘tidal waves’
Composed of a train of waves
CHARACHTERISTICS OF TSUNAMIS
• Long wave periods
• Can achieve extreme
•
•
heights
Are rare events
At open sea, they
travel extremely fast,
reaching velocities of
700 Km/H (400 Mh/H)
WHAT CAUSES TSUNAMIS
•
•
•
•
Sub-marine earthquake
Landslides
Volcanic eruptions
Cosmic – body impacts (asteroids, comets, etc.)
WHAT HAPPENS TO A TSUNAMI AS
IT APPROACHES LAND
• Its height grows due to shoaling
• They lose some energy as they rush onshore
• Depending on the particular beach this makes
surfing possible
SPECULATION ON A MASSIVE
TSUNAMI
• If an asteroid or comet 4 kilometers in diameter were to
strike the earth the resulting wave can make entire
coastlines disappear and wreck havoc on national
infrastructures. If the body were large enough, it would
achieve the status of ELE (Extinction Level Event) and
change our fundamental way of life
THE IMPACT ON HUMANS
• Tsunamis are considered catastrophic events
• They are rare, but very difficult to predict
• The death tolls of an attack can reach tens of
thousands
WAVE RESONANCE
An interesting wave phenomenon is the resonance effect that occurs when
a tsunami, or any other type of wave, comes into indirect contact with another
medium which has the same properties and part of its energy is transferred to
the other medium, thereby ‘resonating’ itself into places which otherwise it
would have been impossible to enter.
WAVE SUPERPOSITIONS
The following mathematical equations
expresses the processes of wave superpositions;
when two waves come together and form a single
one with characteristics of both.
In the picture we see an electronic wave simulator
  wt )
which is showing this kind of phenomenon. y  f ( x  vt)  sin(
2
sin( x  vt)  sin[

( x  vt)]  sin( kx  kvt)  sin( kx  wt )
y  sin( kx  wt  )
k
2

2
w
t
A  amplitude
  wavelength
W  frequency
sup erposition s :
1  2 , a1  a2
cos( k1 x  w1t )  cos( k 2 x  w2t )  2 cos[ kx * sin( wt )]
1  2 , a1  a2
cos( k1 x  w1t )  cos( k 2 x  w2t )  cos(
k1  k 2
w  w2
k k
w  w2
x 1
t ) cos( 1 2 x  1
t)
2
2
2
2
THANKS:
• Ronen Avni for teaching us so very
patiently the material and for his great
examples.
• Technion for letting us use their facilities
• Faculty of civil engineering
• Ami and Guy for driving us around and
help