Wave setup

In fluid dynamics, wave setup is the change in mean water level due to the presence of waves. This setup is present in and near the coastal surf zone, and is evidenced by a rise in mean sea level above the still water line.

Wave setup can be mathematically modeled by considering the variation in radiation stress (Longuet-Higgins & Stewart 1962) in the longshore and cross shore directions. As a progressive wave approaches shore and the water height decreases, there is additional flux of horizontal momentum due to the bottom pressure, but the energy remains constant. The additional flux is balanced by a decrease in the mean water level before the waves break, called a "set down".

After the waves break (see breaking wave), the energy is no longer constant, but decreasing due to energy dissipation after the break point. The radiation stress therefore decreases, and the free surface height increases to balance, causing wave setup. Both of the above descriptions are specifically for beaches with low slope. As the wave approaches shore, the higher mean sea level may lead to wave run-up on the beach.

Wave setup and wave run-up are particularly of concern during storm events, when the effects of big waves generated by wind from the storm are able to do damage to coastal infrastructure because of wave setup and a corresponding increase in mean sea level.

References

• Longuet-Higgins, M. S.; Stewart, R. W. (1962), "Radiation stress and mass transport in gravity waves, with application to 'surf beats'", Journal of Fluid Mechanics 13 (4): 481–504, Bibcode 1962JFM....13..481L, doi:10.1017/S0022112062000877
• Dean, Robert G.; Walton, Todd L. (2009), "Wave setup", in Kim, Young C., Handbook of coastal and ocean engineering, World Scientific, pp. 1–23, ISBN 978-981-281-929-1