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5.3 Waves On a Rip-Channel
Both Birkemeier and Dalrymple (1976) and Ebersole and Dalrymple (1979) examined
the case of waves incident upon a shore with the presence of a rip-channel. The bottom
topography was given according to a formula first used by Noda et al. (1974)
h{x,y) = mx jl + Ae-s^)1/S sin10 ^(y ztan^)| (5.7)
where (3 is the angle the rip-channel makes with the x axis which is, in their coordinate
system, directed offshore from the still water line, m is the beach slope, A is an amplitude
of the bottom variation and A is the length of the repeating beach. The origin of the
coordinates is at the intersection of the still water line and the trough as is shown in
figure 5.5 which gives the depth contours for the case where the slope is .025 and f) is equal
to 30 degrees.
Due to the restriction of the present model that there be no y gradients at the lateral
bound aries the above formulation is modified to be
h(x ) = / ^{i + Ae-W^sin^fiv-ztan/?)} |f (y xtan£)| < *
K [mi | j(y x tan fi)\ > x V '
Also shown in figure 5.5 are the contours obtained through use of the modified Eq. 5.8
for /? equal to 30 degrees and a .025 slope. The two formulas differ only in that the repeating
rip channels in the Noda formulation are removed. For application in the present model the
presence of the trough in the farthest offshore grid row is removed so that the depth in the
offshore grid row remains constant in compliance with the requirements of the boundary
conditions as discussed in sections 4.3 and 4.4.
Figure 5.6 shows the results obtained by Ebersole and Dalrymple for the case of a wave
angle of 30 degrees a wave height of 1.0 meters and a period of 4 seconds. Figure 5.7 gives
the results for the present model. Even though the scales of the two figures are different it
is evident that there is agreement between the two. The length scale of the eddy is about
30 meters for both cases. In the caption to the figure of his results, Ebersole indicated that
the lateral mixing coefficient may have been large. The present author does not believe