Wave shoaling

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Surfing on shoaling and breaking waves.

Wave shoaling.

In fluid dynamics, wave shoaling is the effect in which 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 tsunamis 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.

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[edit] References

Dean, R.G.; Dalrymple, R.A. (1991). Water wave mechanics for engineers and scientists. Advanced Series on Ocean Engineering. 2. Singapore: World Scientific. ISBN 978-9810204204.
Goda, Y. (2000). Random Seas and Design of Maritime Structures. Advanced Series on Ocean Engineering. 15 (2^nd edition ed.). Singapore: World Scientific. ISBN 978 981 02 3256 6.