Associated with the incident waves is a flux of momentum that is parameterized by the wave radiation stress [ Longuet-Higgins and Stewart, 1962]. As the waves dissipate in the surf zone, gradients in this momentum flux force a landward flow until balanced by an opposing pressure gradient. This elevated sea level is known as wave set-up. In principle, this is just the difference frequency interaction of a wave with itself transferring energy to zero frequency (mean flows).
Also associated with the incoming waves is an Eulerian mass flux (more fluid is carried forward under the wave crest than is returned under the trough) that must be balanced below the wave trough level by a seaward return flow known as the undertow [ Dhyr-Nielsen and Sorensen, 1970]. Recent research [ Svendsen, et al., 1987; Deigaard, et al., 1991] on undertow has centered on the role of turbulence in the dissipating bore (parameterized by the wave roller) in undertow dynamics. Since the roller is advected with the bore face, it's presence affects the wave mass transport. Moreover, the interfacial stress between the roller and the underlying bore surface provides a surface stress condition for the water column that, when coupled with the mass balance equations, can be used to solve for undertow profiles.
Waves approaching the beach from an angle carry with them an onshore
flux of alongshore-directed momentum, the familiar 
radiation
stress term. As the incident waves break in the surf zone, this
momentum flux drives a mean longshore current. For natural wave fields
with a distribution of wave heights (each breaking at different
cross-shore locations), this momentum input is spread in the
cross-shore, providing a natural smoothing to the forcing function. On
monotonic beach profiles, simple models for longshore current
generation have been very successful [ Thornton and Guza, 1986].
However, the models break down when applied to a barred beach profile. Instead of the predicted narrow jets over the bar crest and steep foreshore where momentum input is concentrated by breaking, observed currents are broad and often strongest in the trough of the bar (where wave forcing is a minimum). Research has focused on three mechanisms to explain the large mixing and apparent shoreward shift of the forcing pattern.
Shear waves (very low frequency instabilities of the longshore current, discussed in the next section) have associated non-zero Reynold's stresses that act to redistribute momentum in the cross-shore, away from the peak momentum input at the bar crest. It has been suggested that these motions may provide an important mixing mechanism on barred beaches where shear waves should be strongest [ Bowen and Holman, 1989; Dodd and Thornton, 1990]. Initial examinations have shown shear wave mixing to be significant, although probably not sufficiently strong to explain the observations.
Putrevu and Svendsen [1992], made the interesting suggestion that the sheared cross-shore flows (the vertical profile of undertow) will act to significantly broaden the predicted narrow longshore current jet. As a mixing agent, this interaction was found to be an order of magnitude more efficient that horizontal eddy mixing.
Finally, the importance of the wave roller and its associated TKE
content has been investigated as a mechanism for both spreading and
delaying the input of momentum from the incident wave field to the
water column [ Nairn, et al., 1990; Freds
and Deigaard,
1992; Smith, et al., 1993]. The delay due to decay of the
wave-generated turbulent kinetic energy, advected with the progressing
bore, provides a very effective mechanism for offsetting the current
maximum into the bar trough. While this has reduced the discrepency
with observations, the modelling of longshore currents over barred
bathymetries continues to be a challenging problem.