Background of rip currents

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Generation and characteristics of rip currents

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Waves propagate towards the beach and tend to break. In this breaking process the water mass on the surface (or any object like a ball) is carried towards the beach. The water mass must return to the sea somehow to satisfy the continuity equation of mass, ie some form of a return flow must compensate for the landward movement of water. The return flow can have two forms:

From discussions with lifeguards in California Shepard et al. (1941) concluded that the latter is widely evident and must therefore account for most of the return flow. In the field he found three components that together form a rip current (Figure 1) . The first is a feeder current formed by water moving parallel to the shore. The second is a rip neck that is maintained by feeder currents from either side or, in some cases, by a feeder current from one side only. The narrow and offshore directed flow in the rip neck can reach velocities up to 2 m/s. The third component is the rip head in which the flow diffuses and the velocities decrease. Together with the onshore mass transport of water in the breaker zone the rip current forms a closed circulation cell. Floating material only eventually exits this circulation cell and is ejected offshore or is washed on the beach.

The process that drives a rip current is the long-shore non-uniformity of either the wave field or the bottom topography (Bowen, 1969). Wave-wave interactions or long-shore bottom variations induce a long-shore varying wave height. As waves approach shallower water, the waves change in wave height and radiation stress gradients are induced (Longuet-Higgins and Stewart, 1964). The momentum balance equation requires compensation by an opposing water level gradient or a flow induced frictional force. Thus, intense wave breaking results in large radiation stress gradients which in turn generate a high set up at the coast line. Vice versa less wave breaking causes a lower set up at the coastline. These water level gradients are important because such alongshore gradients drive shore parallel flows. Long-shore flows with opposite direction converge at locations with less set up and feed the rip current.

Figure 1. Idealized diagram of a rip current system (NOAA's National Weather Service)

Morphologically controlled rip currents

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Dalrymple et al. (2011) have identified morphologically-controlled rip currents as the most common form. Furthermore they are found to be stronger than their non-morphologically controlled counterparts, the so-called transient rip currents. The location of morphologically controlled rip currents is tied to a rip channel that interrupts the adjacent sand bar. The waves break over the bar and an onshore mass flux over the sand bar is observed. As a result, water "piles up" in the trough between the beach and the bar. In the channel, however, the waves break later and hence, induce less set-up. An alongshore flow along the beach is initiated (by a water level gradient) towards the rip channel where it is deflected offshore. In an experimental study, Haller et al. (2002) observed a second circulation cell (Figure 2) . Closer to the shore, the waves in the rip channel finally break while behind the bar the waves are either smaller or absent. Thus, close to the shore the wave set-up in the rip channel is larger than behind the bar. As a result the water flows away from the rip channel and in the opposite direction of the feeder current.

The channel itself evolves from an initially small bottom perturbation and quickly grows through a feedback mechanism. The offshore current transports sediment from the channel seawards where it is deposited at the rip head. As a result the channel deepens and the rip current becomes enhanced. Rip channels change on the morphological time scale of the beach. For this reason their location can remain constant for as long as several weeks or months until the morphology is reset by a storm event (Wright et al., 1984).Rhythmic bar-and-beach (RBB) and transverse bar-and-rip (TBR)beach states are found to inhibit the highest long-shore variability (Ranasinghe et al., 2004). This implies that rip channels are more defined and rip currents are more intense.

Tidal modulation of rip currents

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Obviously rip current flow is conditional upon wave dissipation. Waves will break over the bar if the ratio of wave height to water depth exceeds a certain value. This implies that rip currents are not only dependent on wave height but also on water level that might be modified by the tide. The strongest rip velocities have been observed at low tide (Aagaard et al., 1997; Brander and Short, 2000; MacMahan et al., 2005) while during high tide, more waves propagate over the bar without breaking and the rip current is weaker or completely inactive.

Low-frequency pulsing of rip currents

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Rip currents are found to pulsate with low frequencies. It is hypothesised that rip pulsations are owned to the effect of wave current interaction (Haas et al., 2003). The offshore directed current slows down wave propagation in the channel. As a result the incident waves steepen and bend towards the centre of the channel due to current refraction. Eventually waves start breaking in the channel and induce wave set-up that reduces the alongshore water level gradient. As the alongshore water level gradient is the main driving mechanism of the rip current, this leads to reduced rip velocities. The weaker rip effects wave propagation less and no wave breaking occurs in the channel anymore. Hence, the current picks up again in strength. This feedback mechanism leads to pulsations of the rip current.

Rip current pulses are believed to cause the infrequent surf zone exits of floating material (MacMahan et al., 2010).

Observations of rip currents

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Shepard et al. (1941) have proposed six features that can be used to identify rip currents in the field.

  1. Sediment laden water indicates the presence of a rip because sediment is transported seawards by the current.
  2. The location of the channel is marked by green water where the depth is larger.
  3. The foam of the breaking waves is carried offshore beyond the breaker line by the rip current.
  4. Choppy water points to locations where currents oppose the incident waves.
  5. In the rip channel the waves break closer to the shore and therefore a gap in the breaker line is observed.
  6. Floating objects can be used to test if an offshore current is present.

Though none of these characteristics alone is sufficient to prove the presence of a rip current, they all together can give a hint to its existence. In the Netherlands not all of these indicators are suitable because the water of the North Sea is often too turbid. In addition to the above mentioned indicators the presence of a rip current can be deduced from a cross pattern in the advancing waves. The incident waves bend towards the rip current due to current refraction and a cross sea forms.

The hostile environment of the surf zone complicates the measurement of rip currents in the field. As a result field data on rip currents is scarce. The first attempt to demonstrate rip currents in the field was done by Shepard et al. (1941) who mapped the drifter paths of floating objects. Other methods to illustrate the flow patterns were used by Brander (1999) such as the release of potassium permanganate dye in the near shore zone. For a quantitative analyse of a rip current, meters were used in various experiments (Dette et al., 1995; Aagaard et al., 1997; Brander, 1999; Brander and Short, 2000; Callaghan et al., 2004; MacMahan et al., 2005; MacMahan et al., 2008; Bruneau et al., 2009). Current meters deployed in cross shore and/or long shore transects provide Eulerian flow measurements. However, the installation of these instruments in the surf zone is problematic. Furthermore, Eulerian measurements have two limitations. Firstly, current meters at a limited number of positions cannot capture the whole flow pattern. Secondly, the measurements cannot depict the spatial variability of rip currents because they are restricted to predefined locations. To overcome these problems surf zone drifters have been developed. In more recent field studies GPS drifters have been used to obtain a more comprehensive image of the flow patterns in a rip current (Johnson and Pattiaratchi, 2004; MacMahan et al., 2010). During his field experiments at Muriwai/New Zealand (Brander and Short, 2000) tracked human drifters by means of two theodolites from the beach. Human drifter paths were also recorded with GPS mounted to the people's heads during the experiments of MacMahan et al. (2010).

The results of GPS drifter tracking showed that the rip current flow is mainly retained in the surf zone (Reniers et al., 2009). Observed flow patterns included eddies and meandering long shore currents.

Modelling of rip currents

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Numerical simulations have been performed to reproduce data obtained in the laboratory and in the field. The experimental study by Haller et al. (2002) has been used to verify three numerical rip current simulations, that are described here:

The first one to mention was performed by Chen et al. (1999) who used a Boussinesq type model to simulate the rip currents measured in the laboratory. He found that the rip current was accompanied by strong vortices and that the flow oscillated in the channel. It was hypothesised that the instabilities of the current in the channel prevent the rip from extending further offshore. The instabilities were associated with small perturbations in the bathymetry of the wave basin. However instabilities also occurred in simulations with a nearly perfect symmetric bathymetry, though they emerged later. These instabilities were believed to stem from computational round off errors.

With a quasi-three-dimensional model, Haas et al. (2003) investigated the influence of bottom friction, wave current interaction and three-dimensional effects on rip current characteristics. Firstly, it was found that an increase in bottom friction stabilises the location of the rip current in the channel and reduces peak velocities. Secondly, wave current interaction proved to be important to reproduce the meandering of the rip in the channel which reduces the offshore extent of the rip current. Thirdly, three-dimensional simulations introduce additional dissipation terms next to turbulent mixing, bottom friction and horizontal shear stresses. It was shown that with the three-dimensional dispersive mixing mechanism eddies dissipated quicker and the flow pattern was more stable.

The most recent study was undertaken by Jacobs (2010) who showed that a non-hydrostatic version of XBeach reproduces the experimental results well. The agreement of the modelled and measured data of water levels and cross-shore currents was better than in previous studies (Chen et al., 1999; Haas et al., 2003). It is noted that a higher grid resolution was used in the XBeach model set-up.

Other numerical studies address the retention and ejection of floating material in the surf zone (Reniers et al., 2009; Reniers et al., 2010). It was demonstrated that Stokes drift accounts for the retention of drifters within the surf zone while very low frequency motions are associated with rip pulses that lead to drifter ejection. In order to reproduce drifter exit rates that were observed in the field (MacMahan et al., 2010), a numerical model needs to comprise both mechanisms, very low frequency motions and Stokes drift which is represented in this model in the Generalized Lagrangian Mean (GLM) velocities.