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current velocity profile as a
restoring force rather than gravity. This wave motion, occurring in the horizontal
plane and moving with a speed somewhat less than the longshore current, causes
the longshore current to move back and forth across the surf zone. Reniers et al.
(1997) demonstrated the existence of shear waves in the laboratory. Dodd, Oltman-
Shay, and Thornton (1992) showed that bottom friction retards the onset of the shear
wave instability, whereas Putrevu and Svendsen (1993) demonstrated that a barred
shoreline reinforces it, which explains why these waves were present at Duck and
not obvious at other field sites on more planar beaches.
Allen, Newberger, and Holman (1996) showed, using a numerical model, that
the incorporation of nonlinear terms allows the shear waves to evolve into large-
amplitude oscillations and to migrate offshore of the surf zone as eddies. This mo-
tion looks very much like unstable rip currents. O¨zkan-Haller and Kirby (1999)
have also modeled this nonlinear behavior, showing the interaction between shear
waves, the offshore detachment of pairs of vortices, and that the shear waves cause
considerable horizontal mixing in the surf zone – even greater than that due to
turbulence.
This topic is still one of considerable interest to nearshore hydrodynamicists.
5.5 NEARSHORE CIRCULATION AND RIP CURRENTS
The nearshore circulation system occurring at the beach often includes nonuniform
longshore currents, rip currents, and cross-shore flows.
Rip currents are jets of water issuing through the breaker line that carry sand off-
shore. These currents can sometimes be observed occurring (somewhat) periodically
down a long straight beach; they also occur under piers, alongside jetties and groins,
in the center of embayments formed by headlands, and at breaks in sandbars and
offshore breakwaters. The offshore velocity in rip currents can exceed 2 m/s, and
they contribute to the death toll at beaches by carrying unwary swimmers directly
offshore into deep water. The general circulation pattern for a rip current system,
with its feeder currents along the beach, is shown in Figure 5.10.
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112 WAVES AND WAVE-INDUCED HYDRODYNAMICS
Figure 5.10 Schematic of a nearshore circulation system
showing the rip current and the feeder currents.
Rip currents on a long straight beach have been observed from one horizon to
the other with roughly a uniform spacing. What creates this longshore periodic phe-
nomena? Several mechanisms could be responsible. First, the offshore bathymetry
may have a periodic spacing, causing periodic refraction of the waves and leading to
periodic variations in setup and the circulation system (Bowen 1969b, Sonu 1972).
This simply backs us up to the question of why there is a variation in the bathymetry.
Is this some edgewave-induced phenomenon (Holman and Bowen 1982)? Alterna-
tively, the incident wave climate may have periodic modulations (Dalrymple 1974,
Tang and Dalrymple 1989) that force the nearshore hydrodynamics. The Dalrymple
model examines crossing wave trains of the same frequency that force a fixed long-
shore variation in wave height and thus wave setup, creating rip currents where
the wave amplitudes cancel out. Fowler and Dalrymple (1990) showed that inter-
secting wave trains with nearly the same period will produce migrating rip current
systems. Both of the intersecting wave models have been tested successfully in the
laboratory. The Tang and Dalrymple concept is that a directional spectrum will have
modulations, as discussed by Gallagher, which will force the nearshore circulation
system.
Zyserman, Fredsøe, and Deigaard (1990) consider rip currents on a coast with
sandbars. The rip current channels and the sediment transport are assumed to be in
balance, and thus the spacing and the depth of the channels can be predicted.
Dalrymple (1978) examined the mechanism for creating rip currents in channels
through offshore bars. He proposed that the wave setup created shoreward of the
sandbar is higher than that created behind the rip channel. Therefore, there is a
longshore gradient of mean water level driving flow toward the channel. Haller,
Dalrymple, and Svendsen (1997) showed in a wave basin that the rip currents do
occur via preestablished channels through longshore sandbars but that these rip
currents are unstable and oscillate side-to-side because of flow instabilities triggered
by the strong shear in the offshore velocity profile. Haller and Dalrymple (2001)
provide a model for this instability based on the shear in the offshore velocity profile
of the rip current.
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5.5 NEARSHORE CIRCULATION AND RIP CURRENTS 113
Table 5.3 Mechanisms for Rip Currents
Wave–Wave Interaction Representative References
Incident Wave–Edge Wave
Synchronous Bowen (1969b)
Infragravity Sasaki (1975)
Intersecting Wave Trains Dalrymple (1975), Fowler and Dalrymple (1990)
Wave–Current Interaction Dalrymple and Lozano (1978)
Wave Structure Interaction
Bottom Topography Bowen (1969b), Zyserman et al. (1990)
Coastal Boundaries
Breakwaters Liu and Mei (1976)
Islands Mei and Angelides (1977)
Barred Coastlines Dalrymple (1978)
Primary Source: Dalrymple (1978).
Other nearshore circulation models examine instabilities and eigenvalue res-
ponses of the surf zone. For example, Dalrymple and Lozano (1978) examined the
case of normally incident waves on a surf zone on a planar beach. One possible
solution to this problem is no circulation with a longshore uniform setup within
the surf zone. Another possibility assumes an existing rip current, which forces the
incident waves, by wave–current interaction, to slow over the rip, causing the waves
to refract toward the rip. This refraction inside the surf zone drives longshore currents
toward the base of the rip, which then flows offshore. This self-reinforcing circulation
pattern provides another stable solution to the flow in the surf zone.
Finally, the presence of structures can lead to rip currents. Liu and Mei (1976)
examined the rip formed behind an offshore breakwater as a result of the wave
diffraction pattern that occurs in this region. Table 5.3 lists several of the various
models for rip currents.
5.5.1 NUMERICAL MODELING OF NEARSHORE CIRCULATION
Numericalmodeling of the nearshore circulation system (including rip and longshore
currents) permits the study of both onshore and offshore motions as well as long-
shoremotions and can in fact include the influenceof rip currents.Avariety ofmodels
has been developed, for example, Noda (1974); Birkemeier and Dalrymple (1975);
Vemulakonda, Houston, and Butler (1982); Kawahara and Kashiyama (1984); Wu
and Liu (1985); and Van Dongeren et al. (1994). These depth-averaged models in
general solve the nearshore circulation field forced by bottom variations, although
Ebersole and Dalrymple (1980) examined the case of intersecting wave trains and
Wind and Vreugdenhil (1986) addressed the circulation induced between two barri-
ers, pointing out the importance of correctly modeling the lateral shear stresses. The
last model by Van Dongeren et al. is quasi-three-dimensional, adding the influence
of the undertow on the longshore current, as pointed out by Putrevu and Svendsen
(1992).
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114 WAVES AND WAVE-INDUCED HYDRODYNAMICS
Madsen, Sørensen, and Schaffer (1997a,b) have shown that an extended
Boussinesq wave model can predict surf zone hydrodynamics quite well when a
wave-breaking algorithm is included. Averaging the numerical model currents over
awave period yields the “mean” flows of the nearshore circulation system.Chen et al.
(1999) compared Boussinesq model results with a physical model of the nearshore
circulation on a barred shoreline with rip channels. The numerical model predicts the
instabilities