Inphysical oceanography,undertow is theundercurrent that moves offshore whilewaves approach the shore. Undertow is a natural and universal feature for almost any largebody of water; it is a return flow compensating for the onshore-directed average transport of water by the waves in the zone above thewave troughs. The undertow'sflow velocities are generally strongest in thesurf zone, where the water is shallow and the waves are high because ofshoaling.^[1]

In popular usage, the wordundertow is often misapplied torip currents.^[2] An undertow occurs everywhere, underneath the shore-approaching waves, whereas rip currents are localized narrow offshore currents occurring at certain locations along the coast and most forceful by the water's surface.^[3][4]

An "undertow" is a steady, offshore-directed compensation flow, which occurs below waves near the shore. Physically, nearshore, the wave-inducedmass flux betweenwave crest andtrough is onshore directed. This mass transport is localized in the upper part of thewater column, i.e. above thewave troughs. To compensate for the amount of water being transported towards the shore, a second-order (i.e. proportional to thewave heightsquared), 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.^[5]

The term undertow is used in scientific coastal oceanography papers.^[6][7][8] The distribution offlow velocities in the undertow over the water column is important as it strongly influences the on- or offshoretransport of sediment. Outside the surf zone there is anear-bed onshore-directed sediment transport induced byStokes drift and skewed-asymmetric wave transport. In the surf zone, strong undertow generates a near-bed offshore sediment transport. These antagonistic flows may lead tosand bar formation where the flows converge near thewave breaking point, or in the wave breaking zone.^[6][7][8][9]

An exact relation for the mass flux of anonlinearperiodic wave on aninviscid fluid layer was established byLevi-Civita in 1924.^[10] In aframe of reference according toStokes' first definition of wave celerity, the mass flux${\displaystyle M_w}$ of the wave is related to the wave'skinetic energy density${\displaystyle E_k}$ (integrated over depth and thereafteraveraged overwavelength) andphase speed${\displaystyle c}$ through:

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

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:^[11]

${\displaystyle \overline{u}=-\frac{2E_k}{\rho ch},}$

with${\displaystyle h}$ the mean water depth and${\displaystyle \rho }$ the fluiddensity. The positive flow direction of${\displaystyle \overline{u}}$ is in the wave propagation direction.

For small-amplitude waves, there isequipartition of kinetic (${\displaystyle E_k}$) andpotential energy (${\displaystyle E_p}$):

${\displaystyle E_w=E_k+E_p\approx 2E_k\approx 2E_p,}$

with${\displaystyle E_w}$ the total energy density of the wave, integrated over depth and averaged over horizontal space. Since in general the potential energy${\displaystyle E_p}$ is much easier to measure than the kinetic energy, the wave energy is approximately${\displaystyle E_w\approx \frac{1}{8}\rho g{H}^2}$ (with${\displaystyle H}$ thewave height). So

${\displaystyle \overline{u}\approx -\frac{1}{8}\frac{g{H}^2}{ch}.}$

For irregular waves the required wave height is theroot-mean-square wave height${\displaystyle H_{\text{rms}}\approx \sqrt{8}\sigma ,}$ with${\displaystyle \sigma }$ thestandard deviation of the free-surface elevation.^[12]The potential energy is${\displaystyle E_p=\frac{1}{2}\rho g{\sigma }^2}$ and${\displaystyle E_w\approx \rho g{\sigma }^2.}$

The distribution of the undertow velocity over the water depth is a topic of ongoing research.^[6][7][8]

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 until the rip releases them. However, drowning can occur when swimmers exhaust themselves by trying unsuccessfully to swim directly against the flow of a rip.

On theUnited 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]

• Longshore current – Sediment moved by the longshore currentPages displaying short descriptions of redirect targets

• Tatiana Morales (2004-05-27),Watch out for rip tides, CBS News, retrieved2015-06-24

• Water waves
• Physical oceanography

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