# Difference between revisions of "Wave run-up"

 Definition of Wave run-up: Wave run-up is the maximum onshore elevation reached by waves, relative to the shoreline position in the absence of waves. This is the common definition for Wave run-up, other definitions can be discussed in the article

## Notes

Wave run-up is an important parameter for assessing the safety of sea dikes or coastal settlements. Wave run-up is the sum of wave set-up and swash uprush (see Swash zone dynamics) and must be added to the water level reached as a result of tides and wind set-up.

By waves is meant: waves generated by wind (locally or on the ocean) or waves generated by incidental disturbances of the sea surface such as tsunamis, seiches or ship waves. Wave run-up is often indicated with the sympol $R$.

For waves collapsing on the beach, the wave run-up can be estimated to first approximation with the formula of Hunt (1959) [1],

$R = \eta_u + H \xi ,$

where $\eta_u$ is the wave set-up, $H$ is the offshore wave height and $\xi$ is the wave similarity parameter,

$\xi = \Large\frac{\tan \beta}{\sqrt{H/L}}\normalsize = T \tan \beta \Large\sqrt{\frac{g}{4\pi H}}\normalsize ,$

where $L = g T^2/(2 \pi)$ is the offshore wave length, $\beta$ is the beach slope and $T$ is the wave period. The horizontal wave incursion is approximately given by $R / \tan \beta$.

## Related articles

Swash zone dynamics
Wave set-up
Swash
Tsunami

## References

1. Hunt, I.A. 1959. Design of seawalls and breakwaters. J. Waterw. Harbors Division ASCE 85: 123–152