fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, wave setup is the increase in

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithme ...

water level Water level, also known as gauge height or stage, is the elevation of the free surface of a sea, stream, lake or reservoir relative to a specified vertical datum.ISO 772: 1996. Hydrometric determinations – Vocabulary and symbols. See also * ...

due to the presence of breaking

waves Waves most often refers to: *Waves, oscillations accompanied by a transfer of energy that travel through space or mass. * Wind waves, surface waves that occur on the free surface of bodies of water. Waves may also refer to: Music * Waves (ban ...

. 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 As ocean surface waves approach shore, they get taller and break, forming the foamy, bubbly surface called ''surf''. The region of breaking waves defines the surf zone, or breaker zone. After breaking in the surf zone, the waves (now reduced in ...

. Besides a spatial variation in the (mean) wave setup, also a variation in time may be present – known as

surf beat Surf or SURF may refer to: Commercial products * Surf (detergent), a brand of laundry detergent made by Unilever Computers and software * "Surfing the Web", slang for exploring the World Wide Web * surf (web browser), a lightweight web brows ...

– causing

infragravity wave Infragravity waves are surface gravity waves with frequencies lower than the wind waves – consisting of both wind sea and swell – thus corresponding with the part of the wave spectrum lower than the frequencies directly generated by forcing ...

radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...

. Wave setup can be mathematically modeled by considering the variation in

radiation stress In fluid dynamics, the radiation stress is the depth-integrated – and thereafter phase-averaged – excess momentum flux caused by the presence of the surface gravity waves, which is exerted on the mean flow. The radiation stresses behave as ...

. Radiation stress is the

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...

of excess horizontal-

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...

flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

es 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 In fluid dynamics, wave shoaling is the effect by which surface waves, entering shallower water, change in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth ...

. 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 Break or Breaks or The Break may refer to: Time off from duties * Recess (break), time in which a group of people is temporarily dismissed from its duties * Break (work), time off during a shift/recess ** Coffee break, a short mid-morning rest ...

, 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.

References

* * * {{fluiddynamics-stub Physical oceanography Water waves