Undertow (water waves)

In physical oceanography, undertow is the under-current that is moving offshore when waves are approaching the shore. Undertow is a natural 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.[1]

In popular usage, the word "undertow" is often misapplied to rip currents.[2] An undertow occurs everywhere underneath shore-approaching waves, whereas rip currents are localized narrow offshore currents occurring at certain locations along the coast. Unlike undertow, rip currents are strong at the surface.

Buhr Hansen and Svendsen ICCE 1984 Fig 1
A sketch of the undertow (below the wave troughs) and the shore-directed wave-induced mass transport (above the troughs) in a vertical cross-section across (a part of) the surf zone. Sketch from: Buhr Hansen & Svendsen (1984); MWS = mean water surface.


An "undertow" is a steady, offshore-directed compensation flow, which occurs below waves near the shore. Physically, nearshore, the wave-induced mass flux between wave crest and trough is onshore directed. This mass transport is localized in the upper part of the water column, i.e. above the wave troughs. To compensate for the amount of water being transported towards the shore, a second-order (i.e. proportional to the wave height squared), offshore-directed mean current takes place in the lower section of the water column. This flow – the undertow – affects the nearshore waves everywhere, unlike rip currents localized at certain positions along the shore.[3]

The term undertow is used in scientific coastal oceanography papers.[4][5][6] The distribution of flow velocities in the undertow over the water column is important as it strongly influences the on- or offshore transport of sediment. Outside the surf zone there is a near-bed onshore-directed sediment transport induced by Stokes drift and skewed-asymmetric wave transport. In the surf zone, strong undertow generates a near-bed offshore sediment transport. These antagonistic flows may lead to sand bar formation where the flows converge near the wave breaking point, or in the wave breaking zone.[4][5][6][7]

Okayasu Shibayama Mimura ICCE 1986 Fig 8
Mean flow-velocity vectors in the undertow under plunging waves, as measured in a laboratory wave flume – by Okayasu, Shibayama & Mimura (1986). Below the wave trough, the mean velocities are directed offshore. The beach slope is 1:20; note that the vertical scale is distorted relative to the horizontal scale.

Seaward mass flux

An exact relation for the mass flux of a nonlinear periodic wave on an inviscid fluid layer was established by Levi-Civita in 1924.[8] In a frame of reference according to Stokes' first definition of wave celerity, the mass flux of the wave is related to the wave's kinetic energy density (integrated over depth and thereafter averaged over wavelength) and phase speed through:

Similarly, Longuet Higgins showed in 1975 that – for the common situation of zero mass flux towards the shore (i.e. Stokes' second definition of wave celerity) – normal-incident periodic waves produce a depth- and time-averaged undertow velocity:[9]

with the mean water depth and the fluid density. The positive flow direction of is in the wave propagation direction.

For small-amplitude waves, there is equipartition of kinetic () and potential energy ():

with the total energy density of the wave, integrated over depth and averaged over horizontal space. Since in general the potential energy is much easier to measure than the kinetic energy, the wave energy is approximately (with the wave height). So

For irregular waves the required wave height is the root-mean-square wave height with the standard deviation of the free-surface elevation.[10] The potential energy is and

The distribution of the undertow velocity over the water depth is a topic of ongoing research.[4][5][6]

Confusion with rip currents

In contrast to undertow, rip currents are responsible for the great majority of drownings close to beaches. When a swimmer enters a rip current, it starts to carry them offshore. The swimmer can exit the rip current by swimming at right angles to the flow, parallel to the shore, or by simply treading water or floating. However, drowning may occur when swimmers exhaust themselves by trying unsuccessfully to swim directly against the flow.

On the United States Lifesaving Association website it is noted that some uses of the word "undertow" are incorrect:

A rip current is a horizontal current. Rip currents do not pull people under the water–-they pull people away from shore. Drowning deaths occur when people pulled offshore are unable to keep themselves afloat and swim to shore. This may be due to any combination of fear, panic, exhaustion, or lack of swimming skills.

In some regions rip currents are referred to by other, incorrect terms such as 'rip tides' and 'undertow'. We encourage exclusive use of the correct term – rip currents. Use of other terms may confuse people and negatively impact public education efforts.[2]

See also

  • Longshore current – A current parallel to the shoreline caused by waves approaching at an angle to the shoreline



  1. ^ Svendsen, I.A. (1984), "Mass flux and undertow in a surf zone", Coastal Engineering, 8 (4): 347–365, doi:10.1016/0378-3839(84)90030-9
  2. ^ a b United States Lifesaving Association Rip Current Survival Guide, United States Lifesaving Association, archived from the original on 2014-01-02, retrieved 2014-01-02
  3. ^ Lentz, S.J.; Fewings, M.; Howd, P.; Fredericks, J.; Hathaway, K. (2008), "Observations and a Model of Undertow over the Inner Continental Shelf", Journal of Physical Oceanography, 38 (11): 2341–2357, Bibcode:2008JPO....38.2341L, doi:10.1175/2008JPO3986.1, hdl:1912/4067
  4. ^ a b c Garcez Faria, A.F.; Thornton, E.B.; Lippman, T.C.; Stanton, T.P. (2000), "Undertow over a barred beach", Journal of Geophysical Research, 105 (C7): 16, 999–17, 010, Bibcode:2000JGR...10516999F, doi:10.1029/2000JC900084
  5. ^ a b c Haines, J.W.; Sallenger Jr., A.H. (1994), "Vertical structure of mean cross-shore currents across a barred surf zone", Journal of Geophysical Research, 99 (C7): 14, 223–14, 242, Bibcode:1994JGR....9914223H, doi:10.1029/94JC00427
  6. ^ a b c Reniers, A.J.H.M.; Thornton, E.B.; Stanton, T.P.; Roelvink, J.A. (2004), "Vertical flow structure during Sandy Duck: Observations and modeling", Coastal Engineering, 51 (3): 237–260, doi:10.1016/j.coastaleng.2004.02.001
  7. ^ Longuet-Higgins, M.S. (1983), "Wave set-up, percolation and undertow in the surf zone", Proceedings of the Royal Society of London A, 390 (1799): 283–291, Bibcode:1983RSPSA.390..283L, doi:10.1098/rspa.1983.0132
  8. ^ Levi-Civita, T. (1924), Questioni di meccanica classica e relativista, Bologna: N. Zanichelli, OCLC 441220095, archived from the original on 2015-06-15
  9. ^ Longuet-Higgins, M.S. (1975), "Integral properties of periodic gravity waves of finite amplitude", Proceedings of the Royal Society of London A, 342 (1629): 157–174, Bibcode:1975RSPSA.342..157L, doi:10.1098/rspa.1975.0018
  10. ^ Battjes, J.A.; Stive, M.J.F. (1985), "Calibration and verification of a dissipation model for random breaking waves", Journal of Geophysical Research, 90 (C5): 9159–9167, Bibcode:1985JGR....90.9159B, doi:10.1029/JC090iC05p09159


External links

Ambient pressure

The ambient pressure on an object is the pressure of the surrounding medium, such as a gas or liquid, in contact with the object.


Anti-fog agents, also known as anti-fogging agents and treatments, are chemicals that prevent the condensation of water in the form of small droplets on a surface which resemble fog. Anti-fog treatments were first developed by NASA during Project Gemini, and are now often used on transparent glass or plastic surfaces used in optical applications, such as the lenses and mirrors found in glasses, goggles, camera lenses, and binoculars. The treatments work by minimizing surface tension, resulting in a non-scattering film of water instead of single droplets. This works by altering the degree of wetting. Anti-fog treatments usually work either by application of a surfactant film, or by creating a hydrophilic surface.

Artificial gills (human)

Artificial gills are unproven conceptualised devices to allow a human to be able to take in oxygen from surrounding water. This is speculative technology that has not been demonstrated in a documented fashion. Natural gills work because nearly all animals with gills are thermoconformers (cold-blooded), so they need much less oxygen than a thermoregulator (warm-blood) of the same size. As a practical matter, therefore, it is unclear that a usable artificial gill could be created because of the large amount of oxygen a human would need extracted from the water.

Blood–air barrier

The blood–air barrier (alveolar–capillary barrier or membrane) exists in the gas exchanging region of the lungs. It exists to prevent air bubbles from forming in the blood, and from blood entering the alveoli. It is formed by the type 1 pneumocytes of the alveolar wall, the endothelial cells of the capillaries and the basement membrane between the two cells. The barrier is permeable to molecular oxygen, carbon dioxide, carbon monoxide and many other gases.

Current (stream)

A current, in a river or stream, is the flow of water influenced by gravity as the water moves downhill to reduce its potential energy. The current varies spatially as well as temporally within the stream, dependent upon the flow volume of water, stream gradient, and channel geometry. In tidal zones, the current in rivers and streams may reverse on the flood tide before resuming on the ebb tide.

Dalton's law

In chemistry and physics, Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This empirical law was observed by John Dalton in 1801 and published in 1802. and is related to the ideal gas laws.

Ekman transport

Ekman transport, part of Ekman motion theory first investigated in 1902 by Vagn Walfrid Ekman, refers to the wind-driven net transport of the surface layer of a fluid that, due to the Coriolis effect, occurs at 90° to the direction of the surface wind. This phenomenon was first noted by Fridtjof Nansen, who recorded that ice transport appeared to occur at an angle to the wind direction during his Arctic expedition during the 1890s. The direction of transport is dependent on the hemisphere: in the northern hemisphere, transport occurs at 90° clockwise from wind direction, while in the southern hemisphere it occurs at a 90° counterclockwise.

Fraction of inspired oxygen

Fraction of inspired oxygen (FiO2) is the fraction of oxygen in the volume being measured. Medical patients experiencing difficulty breathing are provided with oxygen-enriched air, which means a higher-than-atmospheric FiO2. Natural air includes 21% oxygen, which is equivalent to FiO2 of 0.21. Oxygen-enriched air has a higher FiO2 than 0.21; up to 1.00 which means 100% oxygen. FiO2 is typically maintained below 0.5 even with mechanical ventilation, to avoid oxygen toxicity.Often used in medicine, the FiO2 is used to represent the percentage of oxygen participating in gas-exchange. If the barometric pressure changes, the FiO2 may remain constant while the partial pressure of oxygen changes with the change in barometric pressure.


In oceanography, a halocline (from Greek hals, halo- 'salt' and klinein 'to slope') is a subtype of chemocline caused by a strong, vertical salinity gradient within a body of water. Because salinity (in concert with temperature) affects the density of seawater, it can play a role in its vertical stratification. Increasing salinity by one kg/m3 results in an increase of seawater density of around 0.7 kg/m3.

In the midlatitudes, an excess of evaporation over precipitation leads to surface waters being saltier than deep waters. In such regions, the vertical stratification is due to surface waters being warmer than deep waters and the halocline is destabilizing. Such regions may be prone to salt fingering, a process which results in the preferential mixing of salinity.

In certain high latitude regions (such as the Arctic Ocean, Bering Sea, and the Southern Ocean) the surface waters are actually colder than the deep waters and the halocline is responsible for maintaining water column stability, isolating the surface waters from the deep waters. In these regions, the halocline is important in allowing for the formation of sea ice, and limiting the escape of carbon dioxide to the atmosphere.

Haloclines are also found in fjords, and poorly mixed estuaries where fresh water is deposited at the ocean surface.

Neutral buoyancy

Neutral buoyancy occurs when a object's average density is equal to the density of the fluid in which it is immersed, resulting in the buoyant force balancing the force of gravity that would otherwise cause the object to sink (if the body's density is greater than the density of the fluid in which it is immersed) or rise (if it is less). An object that has neutral buoyancy will neither sink nor rise.

In scuba diving, the ability to maintain neutral buoyancy through controlled breathing, accurate weighting, and management of the buoyancy compensator is an important skill. A scuba diver maintains neutral buoyancy by continuous correction, usually by controlled breathing, as neutral buoyancy is an unstable condition for a compressible object in a liquid.


Normocapnia or normocarbia is a state of normal arterial carbon dioxide pressure, usually about 40 mmHg.

Psychrometric constant

The psychrometric constant relates the partial pressure of water in air to the air temperature. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings.

psychrometric constant [kPa °C−1],
P = atmospheric pressure [kPa],
latent heat of water vaporization, 2.26 [MJ kg−1],
specific heat of air at constant pressure, [MJ kg−1 °C−1],
ratio molecular weight of water vapor/dry air = 0.622.

Both and are constants.
Since atmospheric pressure, P, depends upon altitude, so does .
At higher altitude water evaporates and boils at lower temperature.

Although is constant, varied air composition results in varied .

Thus on average, at a given location or altitude, the psychrometric constant is approximately constant. Still, it is worth remembering that weather impacts both atmospheric pressure and composition.

Respiratory quotient

The respiratory quotient (or RQ or respiratory coefficient), is a dimensionless number used in calculations of basal metabolic rate (BMR) when estimated from carbon dioxide production. It is calculated from the ratio of carbon dioxide produced by the body to oxygen consumed by the body. Such measurements, like measurements of oxygen uptake, are forms of indirect calorimetry. It is measured using a respirometer. The Respiratory Quotient value indicates which macronutrients are being metabolized, as different energy pathways are used for fats, carbohydrates, and proteins. If metabolism consists solely of lipids, the Respiratory Quotient is 0.7, for proteins it is 0.8, and for carbohydrates it is 1.0. Most of the time, however, energy consumption is composed of both fats and carbohydrates. The approximate respiratory quotient of a mixed diet is 0.8. Some of the other factors that may affect the respiratory quotient are energy balance, circulating insulin, and insulin sensitivity.It can be used in the alveolar gas equation.

Rip current

A rip current, often simply called a rip (or misleadingly 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.Rip currents can be hazardous to people in the water. Swimmers who are caught in a rip current and who do not understand what is going on, and who may not have the necessary water skills, may panic, or exhaust themselves by trying to swim directly against the flow of water. Because of these factors, rips are the leading cause of rescues by lifeguards at beaches, and rips are the cause of an average of 46 deaths by drowning per year in the United States.

A rip current is not the same thing as undertow, although some people use the term incorrectly when they often mean a rip current. Contrary to popular belief, neither rip nor undertow can pull a person down and hold them under the water. A rip simply carries floating objects, including people, out beyond the zone of the breaking waves.

Science of underwater diving

The science of underwater diving includes those concepts which are useful for understanding the underwater environment in which diving takes place, and its influence on the diver. It includes aspects of physics, physiology and oceanography. The practice of scientific work while diving is known as Scientific diving.

Stratification (water)

Water stratification is when water masses with different properties - salinity (halocline), oxygenation (chemocline), density (pycnocline), temperature (thermocline) - form layers that act as barriers to water mixing which could lead to anoxia or euxinia. These layers are normally arranged according to density, with the least dense water masses sitting above the more dense layers.

Water stratification also creates barriers to nutrient mixing between layers. This can affect the primary production in an area by limiting photosynthetic processes. When nutrients from the benthos cannot travel up into the photic zone, phytoplankton may be limited by nutrient availability. Lower primary production also leads to lower net productivity in waters.

Torricellian chamber

In cave diving, a Torricellian chamber is a cave chamber with an airspace above the water at less than atmospheric pressure. This is formed when the water level drops and there is no way for more air to get into the chamber. In theory such chambers could pose a risk of decompression sickness to divers, similar to flying after diving. Also, in a Torricellian chamber the diver's depth gauge is unlikely to give an accurate reading of pressure as most depth gauges are not designed to show depths less than zero.

The chambers are named after Evangelista Torricelli, inventor of the barometer.


Undertow may refer to:

Undertow (water waves), a strong undercurrent flowing in a different direction from the surface current

Waves and shallow water

When waves travel into areas of shallow water, they begin to be affected by the ocean bottom. The free orbital motion of the water is disrupted, and water particles in orbital motion no longer return to their original position. As the water becomes shallower, the swell becomes higher and steeper, ultimately assuming the familiar sharp-crested wave shape. After the wave breaks, it becomes a wave of translation and erosion of the ocean bottom intensifies.

Ocean zones
Sea level


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