Although the shift in the current distribution obtained by the roller model
is satisfactory, the distribution appears to be somewhat narrow, implying that
the lateral mixing is not sufficient. The present formulation of the mixing
coefficient (Equation 35), where ε depends on H and um, has a tendency to
generate insufficient mixing in the surf zone. In this zone, breaking prevails,
and strong turbulence is generated in the water column enhancing both
vertical and lateral mixing. The next section includes some trial simulations
where mixing produced by the roller is parameterized and incorporated.
Kraus-Sasaki (K&S) Data
Kraus and Sasaki (1979) measured the longshore current distribution
along seven transects on a sandy beach facing the Japan Sea, from which an
average velocity distribution was obtained. The incident waves during the
measurements were clean swell with a significant wave height of 1 m, a mean
wave period of 4.1 s, and a mean wave angle of 9 deg at the point of incipient
breaking. The water depth was measured by rod and transit, and the beach
profile had a step-type shape. No measurements were made of the wave
height variation. Kraus and Larson (1991) discussed the data and the basic
conditions for the numerical simulations more extensively.
Figure 39 compares calculations and measurements (the beach profile is
also shown). The peak in the measured current is fairly well predicted,
whereas the mixing is more pronounced for the measurements in the inner
part of the surf zone where the beach slope is small and the profile has a
shelf-type shape. Also, the offshore tail in the current distribution was
calculated to decay with a smaller gradient than what was observed. The
computations were carried out by Monte-Carlo simulation assuming a
Rayleigh distribution in the offshore. There was no tuning of the parameter
values, but the friction coefficient was changed until the results visually fit
the measurements and the mixing coefficient was held constant (Λ = 0.50).
A friction coefficient value of cf = 0.0035 was obtained if the roller model
was employed and cf = 0.0030 if the roller model was switched off.
As seen from Figure 39, the roller model shifts the peak in the current
toward the shore, improving agreement between calculation and
measurements. However, even after introduction of the roller model, there
are larger disagreements between model and data than for the previous
laboratory simulations, both with respect to the measured offshore tail and
the flat distribution in the surf zone. To improve the agreement and evaluate
the sensitivity of the model to some of the parameters, simulations were made
with different values on βD than were recommended by Dally and Brown
(1995), as well as for alternative mixing formulations.
Figure 40 illustrates the result of changing βD on the longshore current
distribution. A smaller value on βD implies a lower dissipation rate in the
roller, which in turn means that the roller keeps its mass and momentum for a
longer distance, thereby shifting the forcing more shoreward. Thus, the peak
in the current will be translated shoreward if βD is decreased, as seen in
Figure 40. Somewhat better agreement between the calculations and the
59
Chapter 6 Verification of Longshore Current Model