Wave setup

In fluid dynamics, wave setup is the increase in mean water level due to the presence of breaking waves. Similarly, wave setdown is a wave-induced decrease of the mean water level before the waves break (during the shoaling process). For short, the whole phenomenon is often denoted as wave setup, including both increase and decrease of mean elevation. This setup is primarily present in and near the coastal surf zone. Besides a spatial variation in the (mean) wave setup, also a variation in time may be present – known as surf beat – causing infragravity wave radiation.

Wave setup can be mathematically modeled by considering the variation in radiation stress (Longuet-Higgins & Stewart 1962). Radiation stress is the tensor of excess horizontal-momentum fluxes due to the presence of the waves.

In and near the coastal surf zone

As a progressive wave approaches shore and the water depth decreases, the wave height increases due to wave shoaling. As a result, there is additional wave-induced flux of horizontal momentum. The horizontal momentum equations of the mean flow requires this additional wave-induced flux to be balanced: this causes a decrease in the mean water level before the waves break, called a "setdown".

After the waves break, the wave energy flux is no longer constant, but decreasing due to energy dissipation. The radiation stress therefore decreases after the break point, causing a free surface level increase to balance: wave setup. Both of the above descriptions are specifically for beaches with mild bed slope.

Wave setup is particularly of concern during storm events, when the effects of big waves generated by wind from the storm are able to increase the mean sea level (by wave setup), enhancing the risks of damage to coastal infrastructure.

gollark: What would the least terrible way to get the (English) sentence surrounding a position in a string?
gollark: (unless it does and I haven't noticed)
gollark: How come the standard library's `re` doesn't have anything like `findAll` but returning the *positions* of each match?
gollark: I ran my program through `valgrind` to check if it was horribly leaking memory (it doesn't seem to be). It says `Uninitialised value was created by a stack allocation at 0x33DD0A: renderToHtml__rZvmxUK6kmA9c1R4XvQQuAw`, should I be worried?
gollark: I was worried about performance but it seems basically fine.

See also

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
  • Bowen, A. J.; Inman, D. L.; Simmons, V. P. (1968), "Wave 'Set-Down' and Set-Up", Journal of Geophysical Research, 73 (8): 2569–2577, Bibcode:1968JGR....73.2569B, doi:10.1029/JB073i008p02569
  • Dean, Robert G.; Walton, Todd L. (2009), "Wave setup", in Kim, Young C. (ed.), Handbook of coastal and ocean engineering, World Scientific, pp. 1–23, ISBN 978-981-281-929-1
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.