Wave shoaling

Wave shoaling

In fluid dynamics, wave shoaling is the phenomenon that surface waves on a water layer of decreasing depth change their wave height (which is about twice the amplitude). It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth.

In shallow water and parallel depth contours, non-breaking waves will increase in wave height when following a wave packet as it moves from one location towards another location with less water depth. This is for instance particularly important with respect to the devastating effects of tsunami's when they reach the coast.

For non-breaking waves the energy flux associated with the wave motion — which is the product of the wave energy density with the group velocity — between to wave rays is a conserved quantity (i.e. a constant when following the energy of a wave packet from one location to another). As a result, water depth changes result in energy density variations. And wave energy is proportional to the amplitude squared.

See also

* Ocean surface waves
* Airy wave theory
* Shoal
* Dispersion (water waves)
* Ursell number


*cite book | title=Water wave mechanics for engineers and scientists | author=Dean, R.G. | coauthors=Dalrymple, R.A. | year=1991 | series=Advanced Series on Ocean Engineering | volume=2 | publisher=World Scientific | location=Singapore | isbn=978-9810204204
*cite book | first=Y. | last=Goda | title=Random Seas and Design of Maritime Structures | year=2000 | series=Advanced Series on Ocean Engineering | volume=15 | publisher=World Scientific | location=Singapore | edition=2nd edition | isbn=978 981 02 3256 6

External links

* [http://www.encora.eu/coastalwiki/Wave_transformation#Shoaling Wave transformation at Coastal Wiki]

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