Wave shoaling

In fluid dynamics, wave shoaling is the effect by which surface waves, entering shallower water, increase in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, decreases with water depth. Under stationary conditions, a decrease in transport speed must be compensated by an increase in energy density in order to maintain a constant energy flux. Shoaling waves will also exhibit a reduction in wavelength while the frequency remains constant. In other words, as the waves approach the shore and the water gets shallower, the waves get taller, slow down, and get closer together. Particularly in a waterbody shallow enough for its surface to be affected by its bottom and where depth contours parallel the shore, a wave packet that does dissipate its energy by breaking will rise in height as it enters yet shallower water. This is plainly evident for tsunamis as they wax in height when approaching a coastline, often with devastating results.