Undertow
Definition of Undertow:
Undertow is the current flowing offshore near the seabed in the surf zone, mainly driven by wave set-up at the shoreline, and compensating for onshore mass transport by wave crests and wave bores.
This is the common definition for Undertow, other definitions can be discussed in the article
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Notes
The undertow is the offshore-directed, wave-averaged return flow in the surf zone. It forms part of the cross-shore circulation that compensates for the net onshore wave-induced transport in the upper part of the water column. This onshore transport is associated with the phase relation between wave surface elevation and orbital velocity, commonly described as Stokes drift, and with the additional mass transport by breaking-wave rollers and bores; see also wave set-up. Where wave breaking is strongly alongshore non-uniform, part of the return flow can also occur through rip current circulations.
When standing just seaward of the shoreline in strong surf, bathers may feel an onshore surge as a wave crest arrives and a seaward pull near the bed during the following part of the wave cycle. The seaward pull is an undertow component, but should not be confused with the undertow which is the mean offshore flow obtained after averaging over many waves. Undertow is strongest below the wave trough level and above the near-bed wave boundary layer.
There is no generally applicable formula for the undertow velocity, because it depends on wave conditions, water depth, bed slope, bottom roughness, breaking type and shoreface morphology. In idealized alongshore-uniform conditions, the undertow is governed by the wave-averaged cross-shore momentum and mass balances. Important contributions to this balance are the cross-shore gradient of radiation stress, the pressure gradient associated with wave set-up, the momentum flux and shear stress associated with the breaking-wave roller, bottom stress and vertical turbulent mixing.[1][2] Wave set-up results from the decrease of the net onshore wave momentum flux in the surf zone due to wave-energy dissipation, together with the effects of the surface roller and bottom stress[3][4].
Wave dissipation in the surf zone is caused mainly by breaking rather than by bottom friction (see Breaker index). Breaking generates intense turbulence in the upper part of the water column, while turbulence generated by wave orbital motion at the bed is concentrated in the relatively thin wave boundary layer. The vertical distribution of turbulent mixing strongly influences the undertow profile. Strong mixing in the upper water column tends to reduce vertical shear there, whereas the offshore return flow commonly reaches its largest magnitude in the lower part of the water column, above the near-bed boundary layer. This makes undertow important for offshore-directed suspended sediment transport.
A semi-empirical order-of-magnitude estimate for the surf-zone undertow velocity is
[math]\overline{u}_0 \sim 0.1\, c \, H / h\, ,[/math]
where [math]H[/math] is the wave height, [math]h[/math] the water depth and [math]c[/math] the wave celerity[5]. This expression should be regarded only as a rough scaling, because observed undertow velocities depend strongly on the local wave-breaking pattern, morphology and turbulence structure.
Undertow is an important mechanism for offshore sediment transport and beach erosion under storm conditions; see Shoreface profile and Dune erosion. Its erosive effect is enhanced by the strong, more than linear dependence of undertow strength on wave height and by the high suspended sediment concentrations generated by wave breaking[6].
Related articles
- Wave set-up
- Shoreface profile
- Radiation stress
- Breaker index
- Wave transformation
- Shallow-water wave theory
- Currents
References
- ↑ Deigaard, R., Justesen, P. and Fredsoe, J. 1991. Modelling of undertow by a one-equation turbulence model. Coastal Eng. 15: 431-458
- ↑ Stive, M.J.F. and de Vriend, H.J. 1995. Shear stresses and mean flow in shoaling waves. Procs. Coastal Engineering Conf. 1994, Chapter 44
- ↑ Svendsen, I.A. 1984. Wave heights and set-up in a surf zone. Coast. Eng. 8: 303–329
- ↑ Apotsos, A., Raubenheimer, B., Elgar, S., Guza, R.T. and Smith, J.A. 2007. Effects of wave rollers and bottom stress on wave setup. J. Geophysical Research 112, C02003
- ↑ Stive, M.J.F. and Wind, H.G. 1986. Cross-shore mean flow in the surf zone. Coastal Eng. 10: 325–340
- ↑ van der Zanden, J., van der A, D.A., Hurther, D., Caceres, I., O’Donoghue, T. and Ribberink, J.S. 2017. Suspended sediment transport around a large-scale laboratory breaker bar. Coastal Engineering 125: 51–69
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