Water waves

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Water wavesDispersion
Last lecture of the year
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Dispersive waves

• Wave velocity depends on wavelength
• Phase velocity how fast a peak/trough moves.
• Group velocity how fast energy moves.

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Phase velocity gt group velocity
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Phase velocity lt group velocity
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Phase vs. group velocity
Group velocity is fast
Phase velocity is fast
Group velocity is 0
Phase velocity is 0
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Wave parameters
Disclaimer The use of i for the square root of
-1 has not been approved by Gill Pratt or the ECE
community.
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Dispersion relation
The regular wave equation is non-dispersive
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Water wave analysis
?
g

• Conservation of mass
• Lossless flow
• Bernoulli eqn.
• Kinematic condition
• Small amplitude waves
• No surface tension

H
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Particle paths
Deep
Shallow
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Stokes drift
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Shallow and deep water
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Shallow water
Shallow water waves are ordinary waves when
amplitude is small Shallow water wave speed
depends on height of wave results in
breaking Shallow water waves are hyperbolic
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Why are tsunamis shallow water waves?
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Tsunami propagation
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Tsunami propagation
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Deep water waves
Deep water waves are dispersive. Long waves are
faster than short ones. Group velocity is ½ of
the phase velocity.
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Stone in the pond
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Stone in the pond
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Stone in the pond- zoom
Notice that waves magically appear from the
quiet zone!
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Ship wake
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Duck wake
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Ships