Undertow (water waves)

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This article is about undertow beneath water waves near the shore. For other uses, see Undertow (disambiguation).
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.

In physical oceanography, undertow is the steady current – below the splash zone – which is moving offshore for waves approaching a shore. The undertow is the return flow which compensates for the onshore-directed mean mass flow in 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] Undertow can be physically experienced as the offshore current pull that a person standing in the wave-breaking zone can feel most strongly near their feet, as each breaking wave advances towards them.

In popular usage, an undertow is often confused with a rip current.[2] While an undertow occurs everywhere under the shore-approaching waves, rip currents are strong and localized narrow currents occurring at certain locations along the coast.


An "undertow" is a steady, offshore-directed compensation flow below the waves near the shore. Physically, nearshore, the wave-induced mass flux between wave crest and trough is onshore directed. So 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 in coastal sciences: it strongly influences the on- or offshore transport of sediment. Regularly, 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, the 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.[7][4][5][6]

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[edit]

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 M_w of the wave is related to the wave's kinetic energy density E_k (integrated over depth and thereafter averaged over wavelength) and phase speed c through:

M_w = \frac{2E_k}{c}.

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]

\bar{u} = - \frac{2 E_k}{\rho c h},

with h the mean water depth and \rho the fluid density. The positive flow direction of \bar{u} is in the wave propagation direction.

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

E_w = E_k + E_p \approx 2 E_k \approx 2 E_p,

with E_w the total energy density of the wave, integrated over depth and averaged over horizontal space. Since in general the potential energy E_p is much easier to measure than the kinetic energy, the wave energy is approximately {E_w\approx\tfrac18\rho g H^2} (with H the wave height). So

\bar{u}\approx -\frac18 \frac{g H^2}{ c h }.

For irregular waves the required wave height is the root-mean-square wave height H_\text{rms}\approx\sqrt{8}\;\sigma, with \sigma the standard deviation of the free-surface elevation.[10] The potential energy is E_p=\tfrac12\rho g \sigma^2 and E_w\approx\rho g \sigma^2.

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

Confusion with rip currents[edit]

Main article: Rip current

In popular usage, the word "undertow" is sometimes used correctly, in the same sense it is in oceanography. However the term "undertow" is also often used incorrectly, in the mistaken belief that near beaches there is a water flow or current that can pull a person down vertically and hold them underwater until they drown. This misconception stems from a basic lack of knowledge about water currents, and from confusing undertow (which is usually not dangerous) with the more substantial dangers of rip currents. Rip currents also cannot pull a person down, but they can carry a person out beyond the zone of the breaking waves.

In popular use the word "undertow" is sometimes applied to rip currents, which are responsible for the great majority of drownings close to beaches. When a swimmer enters a rip current, it starts to carry the person offshore. If the swimmer understands how to deal with this situation, he or she can easily exit the rip current by swimming at right angles to the flow, in other words swimming parallel to the shore, or by simply treading water or floating. However, if the swimmer does not know these simple solutions, or does not possess the necessary water skills, they may panic and drown, or they may exhaust themselves by trying unsuccessfully to swim directly against the flow.

On the United States Lifesaving Association website it is explained 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]

In popular culture[edit]

In the book The World According to Garp by John Irving, Garp's son thinks that the undertow is an under-toad, a mysterious creature who lives in the sea.

See also[edit]



  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, 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: 2341–2357, doi:10.1175/2008JPO3986.1 
  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, 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, 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, doi:10.1098/rspa.1983.0132 
  8. ^ Levi-Civita, T. (1924), Questioni di meccanica classica e relativista, Bologna: N. Zanichelli, OCLC 441220095 
  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, 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, doi:10.1029/JC090iC05p09159 


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