in which Q is the total volume transport rate in kg/s, d is sediment grain size, and m is
beach slope. . Kamphuis (1991) modified Equation 2 based on laboratory data and re-
analysis of existing field data to include the influence of wave period and give Q in m3/yr:
Q = 6.4 x10 4 H b2T p .5 m 0.75 d -0.25 sin 0.6 (2θ b )
1
(3)
Kraus, et al. (1988) used a different approach and assumed that the total rate of
longshore sediment transport in the surf zone is proportional to the longshore discharge of
water. They found:
Q ∝ K d ( R - Rc )
(4)
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 the discharge parameter,
which can be accurately measured in the LSTF and calculated in the field as:
R = nVls xb H b
(5)
in which n is a constant, Vls is the average longshore current velocity, and xb is the surf-
zone width. Based on field data, Kraus, et al. suggest Kd = 2.7 and Rc = 3.9 m3/s.
Table 2 lists measured transport rates and the values of the predictive equations. The
CERC equation over-predicts the total rate for spilling waves by over 700 percent and
plunging waves by nearly 250 percent. It is interesting to note that the other equations may
predict transport rate for one breaker type well, but none predict values that estimate both
types well. In fact, with the exception of Kamphuis (1991), which includes wave period,
the predictions do not reflect differences between breaker types.
Table 2. Comparison of Measured and Predicted
Transport Rates
Plunging Case
Spilling Case
m3/yr
m3/yr
Transport Rates
Measured
2,660
7,040
CERC formula
22,030
23,850
Kamphuis (1986)
10,760
9,100
Kamphuis (1991)
2,200
5,360
Kraus (1988)
2,670
3,150
Measured sediment flux and an energy dissipation parameter were plotted as a function
of cross-shore location for plunging and spilling breakers in Figures 6 and 7, respectively.
The dissipation parameter was calculated by multiplying longshore velocity by the
difference in energy, i.e., the difference in H2, divided by distance between cross-shore
measurement locations. Figure 6 shows a sharp increase in sediment flux corresponding to
a peak in energy dissipation for plunging waves. Although dissipation is less for the
spilling
Smith and Wang
1225
Previous Page
