circulation cells that included rips. The rip currents were well correlated with
edge waves, the rips occurring at alternate antinodes of displacement of the edge
waves. The spacing of the rip currents was therefore equal to the longshore
wavelength of the edge waves. Field observations made in the Gulf of California
suggest that this mechanism acts on natural beaches.
Hino (1974) developed a second wave interaction model. The formation of a
nearshore circulation system with rips was shown to be the result of
hydrodynamic instability caused by radiation stresses. The instability model is
based on a feedback between the deforming bottom and the flow field. The Hino
(1974) theory predicts rip current spacing to be about four times the surf zone
width. McKenzie (1958) was the first to observe the correlation of rip current
spacing with the width of the surf zone.
Sasaki (1974) investigated the applicability of the Bowen and Inman (1969)
and Hino (1974) theories by describing them with the surf-similarity parameter,
ξ. Sasaki (1974) found that the edge wave theory of Bowen and Inman (1969)
can be applied if ξ is greater than unity. The instability theory of Hino (1974)
gave a good circulation pattern estimate for values of ξ between about 0.23 and
1.0. Sasaki (1975) then developed a theory on rip current spacing based on the
concept of infra-gravity waves when ξ is less than 0.23 and found rip current
spacing (Yr) to be:
Yr = 157ξ02
(0.23 > ξo > 0.08)
(C1)
with
tan β
ξ0 =
(C2)
( H0
L0 )
0.5
where tanβ = beach slope, and H0 = deepwater wave height.
A wave interaction model introduced by Dalrymple (1975) proposed that the
spatial variation in the setup and setdown, caused by intersecting wave trains of
the same period, creates longshore variations in wave height and the mean water
level on the open coast. Currents flow from regions of high setup, or high waves,
to regions of low waves where they flow offshore in a rip current. The predicted
spacing of the rip currents caused by intersecting wave trains is:
L0
Yr =
(C3)
( sin θ0 - sin ζ 0 )
where θ0 and ζ0 = the deepwater wave ray angles of the intersecting wave trains,
measured clockwise from a shore-normal axis. An analysis by Dalrymple and
Lozano (1978) showed that wave-current interaction can support steady state rip
current circulation, but could not treat the initiation mechanism.
C3
Appendix C
Literature Review of Cross-Shore Sediment Transport by Rip Currents
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