ERDC/CHL CHETN-II-46
March 2002
where m is beach slope, Lo is deepwater wavelength, and Hbrms is the root-mean-square breaker
height. Galvin (1968) found that ξb is typically less than 0.4 for spilling breakers. For plunging
breakers, ξb typically ranges from 0.4 to 2.0. A possible relationship between longshore
sediment transport rate and the surf-similarity parameter has been discussed in several studies
(e.g., Kamphuis and Readshaw 1978; Vitale 1981; Ozhan 1982; Bodge 1986; Bodge and Kraus
1991). Kamphuis and Readshaw (1978) and Kamphuis et al. (1986) attempted to incorporate the
surf similarity parameter into the empirical coefficient in the CERC formula. The development
of the Kamphuis-86 and Kamphuis-91 formulas is related to this effort.
In comparison, Kraus, Gingerich, and Rosati (1988) adopted a different approach, which
assumes proportionality between the LST rate and longshore wave-energy flux. Kraus,
Gingerich, and Rosati (1988) assume that the total rate of LST in the surf zone is proportional to
the longshore discharge of water:
Q ∝ K d ( R - Rc )
(5)
where Kd is an empirical coefficient that may relate to sediment suspension, Rc is a threshold
value for significant longshore sand transport, and R is called the discharge parameter and is
proportional to the average discharge of water moving alongshore. Based on field data collected
using streamer sediment traps at Duck, N.C., Kraus, Gingerich, and Roasti (1988) suggested a Kd
value of 2.7 and Rc value of 3.9 m3/sec.
WAVE AND BEACH CONDITIONS: Irregular waves with a relatively broad spectral shape,
representing typical sea conditions, were generated in the LSTF for both spilling and plunging
breakers. The significant breaking wave height, peak spectral period, and mean direction at
breaking were 0.27 m, 1.5 sec, and 6.5 deg for the spilling wave case, and 0.24 m, 3.0 sec, and
6.4 deg for the plunging wave case. The surf similarity parameter ξb for the spilling breaker was
determined to be 0.14, within the range of less than 0.4 as defined by Galvin (1968). However,
the ξb determined for the plunging breaker was only 0.20, much less than the range of 0.4 to 2.0
as suggested by Galvin (1968). This is influenced by the presence of a substantial bar under the
plunging breakers. It is worth noting that the beach slope was determined as the slope between
the depth at the main breaker line and the still-water shoreline. Due to the existence of a
pronounced breakpoint bar that formed for the plunging wave case, the beach slope under the
plunging breaker was substantially gentler than that under the spilling breaker, which resulted in
a smaller ξb. However, if the bottom of the trough is used to calculate the slope, the surf
similarity parameter increases to 0.33.
The LSTF beach is comprised of very well-sorted sand, with a median grain diameter of
0.15 mm. Measurements of LST were made after the beach reached a near-equilibrium
condition, under the prolonged influence of the prescribed incident wave conditions.
Equilibration was reached after 14 hr of wave runs for the spilling breakers. The adjustment to
equilibrium took only 4 hr for the much more energetic plunging breakers (because of the greater
wave period). The equilibrium beach conditions for the two wave cases are shown in Figure 1.
The cross-shore distribution of measured significant wave height at equilibrium is shown in
Figure 2.
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