physics of tsunamis presentation

8/22/2019 Physics of tsunamis presentation

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Wind Waves


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Tsunami


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Water Wave ParametersWavelength

Depth

Amplitude


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Wind Waves parametersm20010~

kmH 4~ HA

mA 101.0~2

Wavelength

Depth

Amplitude

Wind wave parameters in the open ocean


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Tsunami Parameterskm200~

kmH 4~ HA

mcmA 11~2

Wavelength

Depth

Amplitude

Tsunami parameters in the open ocean


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Its All in theWavelength


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Shallow Vs. Deep Water Waves)(2 kHTanhgk

gk

2

22

kgH

1kH 1kH


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Stages of a tsunamiFirst stage: tsunami generation.

Second stage: tsunamipropagation.

Third stage: tsunami run-up onthe coast.


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Tsunami Formation


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Seismic tsunami formation


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Tsunami propagationThe tsunami propagates at

Propagation is linear and without dispersion

or dissipation.Variations in ocean depth change the path

of the tsunami.

At H=4000m v=200 m/s

At H=40m v=20 m/s

gHv


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Tsunami propagation


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Tsunami propagationexamples


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Chile22 May 1960~19:00 GMT

Japan23 May 1960~17:00 GMT

http://www.youtube.com/watch?v=0yha559FvaY&feature=fvwrel
http://www.youtube.com/watch?v=0yha559FvaY&feature=fvwrelhttp://www.youtube.com/watch?v=0yha559FvaY&feature=fvwrel


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Run-up on the shore General concept:

The total wave energy is twice the potential energy and itis conserved:

So:

constAHgdtgHgdxgE

T

22/12/3

0

2

0

2 2/1

4/1HA


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Run-up on the shore Three types of run-ups:

1. Spilling-The crest of the wave breaks,

foam flows down its frontal

slope.

Peculiar to gently slopingbottoms.

http://www.youtube.com/watch?v=IuUygn7BZis
http://www.youtube.com/watch?v=IuUygn7BZishttp://www.youtube.com/watch?v=IuUygn7BZis


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2. SurgingWave floods coast without

breaking.

Peculiar to steep slopes.

http://www.youtube.com/watch#!v=Gbq412haY1c
http://www.youtube.com/watchhttp://www.youtube.com/watch


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3. Plunging-The crest of the wave surpasses

its foot and curls down.

Peculiar to inclined bottom

slopes.

http://www.youtube.com/watch?v=68CLqn28_bY
http://www.youtube.com/watch?v=68CLqn28_bYhttp://www.youtube.com/watch?v=68CLqn28_bY


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Tsunami detectionCoastal measurement: eye witnesses


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Tsunami detectionCoastal measurement(mareographs)


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Tsunami detectionCoastal measurement : geomorphological evidence


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Tsunami detectionDeep-water measurement:Buoy stations


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Tsunami detectionDeep-water measurement:Seafloor observatories


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Summary Tsunamis are characterized by their long

wavelength.

In the open sea tsunamis are linear waves. Changes in the sea bed change the tsunami path.

The tsunami becomes slower and larger whenhitting the shore.

Detecting the tsunami at the open sea is anexperimental challenge.


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A final word of advice


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was the premise put forward clearly and in an attractive way?

were the goals reached?

was the talk clear?

was the presentation style interesting?

what was the quality of the slides?

did the talk fit in its time limits?

are we going to remember some of it (later)?


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Ray Method The ray method can be used to predict the path of the

tsunami:

krvr )( )(rvkk


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Tsunami detectionDeep-water measurement:Satellite altimetry


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Tsunami propagationlimiting processes

Non-lineraity:

At first approximation if we want to take into accountnon-linearity we get:

so the characteristic scale on which non-linear effectswill show will be:

since A


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Dispersion:

The full gravity wave dispersion relation is:

thus:

so the characteristic length for dispersion is


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Damping:

Linear damping due to energy damping within thethin bottom layer can be estimated to be

so the characteristic length the wave travels is

Energy loss related to non-linear damping due to

turbulence can be estimated by giving acharacteristic length


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Damping:


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Seismic tsunami formation-

relevant time scales - the time interval in which the ground deformation occurs at

a point in space. Thdhalf of the time interval in which the ground deformation

occurs over the whole source.

0=(H/g)1/2the propagation time of a long gravitational waveover the ocean depth (020 s for H=4 km)

T0=4H/cSis the maximum period of normal elastic oscillationsof a water layer.

For a source of length RTS:

TTS=RTS (gH)-1/2is the propagation time of long gravitationalwaves across the source. This determines the period of the actualtsunami.

TS=RTS/cS is the propagation time of a hydroacoustic waveacross the source.


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Seismic tsunami formation-

relevant time scales


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Run-up on the shoresimple modelA simple 1D model:


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Run-up on the shoresimple modelWe write down the NS and the continuity eqs:

We go to dimensionless parameters:


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Run-up on the shoresimple modelWe get dimensionless equations:

The dimensionless parameter

determines the dynamics with transition to wavebreaking at


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Seismic tsunami formation- a simple

mathematical modelAssuming water to be an ideal incompressible liquid

and the initial depth H to be constant. We can obtainthe following equations for the small deformation:

The liquid surface deformation

The basin surface deformation


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Their solution is:

with

Seismic tsunami formation- a simple

mathematical model


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Bibliography Physics of Tsunamis, Levin B. & Nosov M., Springer

(2009)

JAMSTEC website.

USGS NEIC website.

Global tectonics and space geodesy, Gordon R.G &Stein S, Science 256, 5055 (1992)

physics of tsunamis presentation

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