Tsunami

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Tsunamis

• Basics
• The Tsunami window
• What determines the wavelength
• Three stages of problem
• Modelling
• References

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Basics

• A Tsunami is a long gravity wave, following the
  linear form of the shallow water equations

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The Tsunami window wavelengths 10 500
km Periods 100 to 2000 seconds (2 30 minutes)
Plot of phase speed, group velocity, wavelength
Ward (2004-5?)
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December 2004 Tsunami Wavelength on open
ocean approx 500 to 800 km, as observed by
TOPEX/Poseidon and Jason-1 (radar) satellites New
Scientist (on web) 6 January 2005 (copy in my
home directory on gale gale /bm/ghome/jmb/tsuna
mis
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What determines the wavelength?

• Answer The dimensions of the original
  ocean-floor perturbation/earth-quake
• Two approaches
• -a) Ward Wave-number spectrum of seafloor uplift
• b) Carrier mathematical/analytical model

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Carrier Model

• Solved Tsunami generation and propagation as an
  initial boundary value problem for a forced wave
  equation (The Cauchy-Poisson problem).
• As described by Gill (1982), p. 178

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Carrier, 1971
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Three stages of problem

• Generation
• Propagation, including dispersion and geometric
  spreading
• Interaction with the continental shelf shoaling
  and run-up

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References

• Gill (1982) Atmosphere-Ocean dynamics basic wave
  theory
• LeBlond and Myask (1978) Waves in the Ocean. The
  dynamics of wave propagation, tsunami generation,
  some treatment of shoaling
• Ward (2004/2005) Tsunamisgt For publication in
  Encyclopedia of Physical Science and
  Technology/Academic Press Available on gale
  /bm/ghome/jmb/tsunamis
• Carrier, 1971 The Dynamics of Tsunamis. In
  Mathematical problems in the Geophysical
  Sciences. Amer. Math. Soc. (In Bureau Library)
• Voit, 1987 Tsunamis Ann Rev. Fluid Dynamics.
  1987 (Bureau Libarary)
• Bryant, 2001 Tsunamis, the underrated hazard
  Bureau Library
• Mander, 1974 Jnl Pysical Oceanography Numerical
  Simulation of Tsunamis --- Classic Paper, carries
  out experiments on shoaling.
• Titov Gonzalez, 1997 NOAA Technical Memorandum
  ERL-PMEL-112. Description of the MOST Tsunami
  generation, prpagation and shoaling model used by
  effectively all US Government agencies (also at
  /bm/ghome/jmb/tsunamis )