# Wave setup

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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.

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 and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation,

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean.

Water level or gauge height or stage is the elevation of the free surface of a stream, lake or reservoir relative to a specified vertical datum.

## Contents

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 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 a second-order tensor.

In mathematics, a tensor is a geometric object that maps in a multi-linear manner geometric vectors, scalars, and other tensors to a resulting tensor. Vectors and scalars which are often used in elementary physics and engineering applications, are considered as the simplest tensors. Vectors from the dual space of the vector space, which supplies the geometric vectors, are also included as tensors. Geometric in this context is chiefly meant to emphasize independence of any selection of a coordinate system.

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If m is an object's mass and v is the velocity, then the momentum is

## 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".

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. Under stationary conditions, a decrease in transport speed must be compensated by an increase in energy density in order to maintain a constant energy flux. Shoaling waves will also exhibit a reduction in wavelength while the frequency remains constant.

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.

In fluid dynamics, a breaking wave is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be transformed into turbulent kinetic energy. At this point, simple physical models that describe wave dynamics often become invalid, particularly those that assume linear behaviour.

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.

## Related Research Articles

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

A rip current, often simply called a rip, or by the misnomer rip tide, is a specific kind of water current which can occur near beaches with breaking waves. A rip is a strong, localized, and narrow current of water which moves directly away from the shore, cutting through the lines of breaking waves like a river running out to sea, and is strongest near the surface of the water.

Parasitic drag is drag that results when an object is moved through a fluid medium. In the case of aerodynamic drag, the fluid medium is the atmosphere. Parasitic drag is a combination of form drag, skin friction drag and interference drag. The other components of total drag, induced drag, wave drag, and ram drag, are separate types of drag, and are not components of parasitic drag. Parasitic drag does not result from the induction of lift on the body, hence it is considered parasitic.

Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters.

Quicksand is a colloid hydrogel consisting of fine granular material, and water.

The surface layer is the layer of a turbulent fluid most affected by interaction with a solid surface or the surface separating a gas and a liquid where the characteristics of the turbulence depend on distance from the interface. Surface layers are characterized by large normal gradients of tangential velocity and large concentration gradients of any substances transported to or from the interface.

In fluid dynamics, wind waves, or wind-generated waves, are surface waves that occur on the free surface of bodies of water. They result from the wind blowing over an area of fluid surface. Waves in the oceans can travel thousands of miles before reaching land. Wind waves on Earth range in size from small ripples, to waves over 100 ft (30 m) high.

Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must decrease continuously or discontinuously with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical distance, the waves propagate horizontally like surface waves, but do so at slower speeds as determined by the density difference of the fluid below and above the interface. If the density changes continuously, the waves can propagate vertically as well as horizontally through the fluid.

Coastal morphodynamics refers to the study of the interaction and adjustment of the seafloor topography and fluid hydrodynamic processes, seafloor morphologies and sequences of change dynamics involving the motion of sediment. Hydrodynamic processes include those of waves, tides and wind-induced currents.

Swash, or forewash in geography, is a turbulent layer of water that washes up on the beach after an incoming wave has broken. The swash action can move beach materials up and down the beach, which results in the cross-shore sediment exchange. The time-scale of swash motion varies from seconds to minutes depending on the type of beach. Greater swash generally occurs on flatter beaches. The swash motion plays the primary role in the formation of morphological features and their changes in the swash zone. The swash action also plays an important role as one of the instantaneous processes in wider coastal morphodynamics.

In fluid dynamics, a Stokes wave is a non-linear and periodic surface wave on an inviscid fluid layer of constant mean depth. This type of modelling has its origins in the mid 19th century when Sir George Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for non-linear wave motion.

In fluid dynamics, Airy wave theory gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational. This theory was first published, in correct form, by George Biddell Airy in the 19th century.

Internal tides are generated as the surface tides move stratified water up and down sloping topography, which produces a wave in the ocean interior. So internal tides are internal waves at a tidal frequency. The other major source of internal waves is the wind which produces internal waves near the inertial frequency. When a small water parcel is displaced from its equilibrium position, it will return either downwards due to gravity or upwards due to buoyancy. The water parcel will overshoot its original equilibrium position and this disturbance will set off an internal gravity wave. Munk (1981) notes, "Gravity waves in the ocean's interior are as common as waves at the sea surface-perhaps even more so, for no one has ever reported an interior calm."

In physical oceanography, undertow is the under-current that is moving offshore when waves are approaching the shore. Undertow is a necessary and universal feature for almost any large body of water: it is a return flow compensating for the onshore-directed average transport of water by the waves in the zone above the wave troughs. The undertow's flow velocities are generally strongest in the surf zone, where the water is shallow and the waves are high due to shoaling.

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 through the wind.

In fluid dynamics, wave–current interaction is the interaction between surface gravity waves and a mean flow. The interaction implies an exchange of energy, so after the start of the interaction both the waves and the mean flow are affected.

The flow in many fluids varies with density and depends upon the gravity. Due to which the fluid with lower density is always above the fluid with higher density. Stratified flows are very common such as the Earth's ocean and its atmosphere.

In fluid dynamics, Green's law describes the evolution of non-breaking surface gravity waves propagating in shallow water of gradually varying depth and width. The law is named after George Green. In its simplest form, for wavefronts and depth contours parallel to each other, it states:

## 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., Handbook of coastal and ocean engineering, World Scientific, pp. 1–23, ISBN   978-981-281-929-1

Michael Selwyn Longuet-Higgins FRS was a mathematician and oceanographer at the Department of Applied Mathematics and Theoretical Physics (DAMTP), Cambridge University, England and Institute for Nonlinear Science, University of California, San Diego, USA. He was the younger brother of H. Christopher Longuet-Higgins.

The bibcode is a compact identifier used by several astronomical data systems to uniquely specify literature references.

In computing, a Digital Object Identifier or DOI is a persistent identifier or handle used to identify objects uniquely, standardized by the International Organization for Standardization (ISO). An implementation of the Handle System, DOIs are in wide use mainly to identify academic, professional, and government information, such as journal articles, research reports and data sets, and official publications though they also have been used to identify other types of information resources, such as commercial videos.