The increase in mean water level due to the presence of breaking waves
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.[1][2]
Wave setup can be mathematically modeled by considering the variation in radiation stress.[3] Radiation stress is the tensor of excess horizontal-momentum fluxes due to the presence of the waves.[4][5]
^Henderson, Stephen M. (2002). "Observations of surf beat forcing and dissipation". Journal of Geophysical Research. 107 (C11): 3193. Bibcode:2002JGRC..107.3193H. doi:10.1029/2000JC000498. ISSN 0148-0227. Retrieved 26 June 2023.
^Wunk, W. H. (1949). "Surf beats". Transactions, American Geophysical Union. 30 (6): 849–854. Bibcode:1949TrAGU..30..849W. doi:10.1029/TR030i006p00849. ISSN 0002-8606. Retrieved 26 June 2023.
^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, S2CID 117932573
^Lentz, Steve; Raubenheimer, Britt (1999-11-15). "Field observations of wave setup". Journal of Geophysical Research: Oceans. 104 (C11): 25867–25875. Bibcode:1999JGR...10425867L. doi:10.1029/1999JC900239.
^Dolata, L. F.; Rosenthal, W. (1984). "Wave setup and wave-induced currents in coastal zones". Journal of Geophysical Research. 89 (C2): 1973. Bibcode:1984JGR....89.1973D. doi:10.1029/JC089iC02p01973. ISSN 0148-0227. Retrieved 26 June 2023.
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