mentioned, Chawla and Kirby (1998, 2002) observed that a nonlinear
dispersion relation was needed to describe blocking on the current, implying
that the linear dispersion relation in NMLong-CW would not be sufficient for
simulating with complete accuracy the measured wave transformation.
Figures 8, 9, 10, and 11 show comparisons of the calculations with the
measurements for Tests M3, M4, M11, and M18, respectively. The x-axis
was defined in the opposite direction compared to C&K in order to make the
waves propagate towards the x-axis, in accordance with the definition in
NMLong-CW. Test M3 represents a case where the waves shoal on the
current and are blocked before breaking occurs (Figure 8). The calculation
agrees well with the measurements during the initial part of the shoaling, but
blocking is predicted to occur more seaward (i.e., at larger x-values) than
what was measured. Chawla and Kirby (1998) attributed this to amplitude
dispersion, where the wave height caused an increase in the phase speed,
implying that a larger current is needed to block a specific wave. It should be
noted that the wave height at blocking is well predicted, although the point of
blocking is displaced somewhat seaward.
Test M4 and M11 illustrate situations where the waves shoal and break
on the current (Figures 9 and 10, respectively). Blocking occurs after some
distance of breaking in Test M4, but not in Test M11, for which the waves
penetrated the area of maximum current even after the reduction in wave
height because of breaking. NMLong-CW satisfactorily predicts the shoaling
phase seaward of breaking, but because of the linear dispersion relation the
point of incipient breaking occurs seaward of the measurements. The wave
height at incipient breaking is also somewhat overestimated, which might be
remedied by modifying the criterion given by Equation 12. The calculations
yield blocking shortly after breaking for both tests, contrary to the
experimental results. After breaking, the predicted wave height decay is
large but seems to be in agreement with the observed gradient, indicating that
the algorithm for determining the wave energy dissipation due to breaking
produces reasonable estimates.
Test M18 involved shoaling and breaking on a current and without
blocking taking place, which was also obtained theoretically employing
linear dispersion. Thus, NMLong-CW did not predict blocking, and the
waves were calculated to propagate through the current everywhere.
Figure 11 shows the comparison between calculations and measurements for
Test M18. The shoaling phase is well described, but incipient breaking
occurs too far seaward, similar to the other simulated monochromatic tests.
Wave height decay is steep, but the gradient is in agreement with the
measurements, at least during the initial phase of breaking. During the later
phase of breaking, the measured wave height decay is more gradual,
indicating the approach towards a stable wave height. The stable wave height
predicted by the model is too low and underestimates the actual stable wave
height with about 30 percent. Thus, in this case the generalization of
Equation 15 to larger water depths yields considerable deviations with
respect to the measurements. In fact, looking at other cases from the C&K
data, it appears that the measured stable wave height is more related to the
incipient breaking wave height than to Hb determined by the local conditions
at any given point. No effort was made here to develop an expression for Hs
that would fit the measurements better than Equation 16.
31
Chapter 4 Verification of Wave Model
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