In fluid dynamics

Fluid dynamics

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

, wave setup is the change in mean

Arithmetic mean

In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...

 water level due to the presence of waves. This setup is primarily present in and near the coastal surf zone

Surf zone

As ocean surface waves come closer to shore they break, forming the foamy, bubbly surface we call surf. The region of breaking waves defines the surf zone. After breaking in the surf zone, the waves continue to move in, and they run up onto the sloping front of the beach, forming an uprush of...

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

Infragravity wave

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

 radiation

Radiation

In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...

.

Mathematically, wave setup can be modelled through the spatial (and temporal) variations in radiation stress

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...

 . These variations are due to the changes in wave height

Wave height

In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighbouring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering....

 by shoaling

Wave shoaling

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

 and breaking.