! Nearshore transformations are dominated by conservative processes (refraction, shoaling, and

diffraction) and hence nonconservative effects (energy sinks and sources) can be neglected as a first

approximation.

(c) A corollary to the first assumption above is that increased accuracy in deterministic propagation

estimates translates into commensurate increases in accuracy in real-world applications. Unfortunately,

laboratory studies by Thompson and Vincent (1984) and Vincent and Briggs (1989) have clearly

demonstrated that the first assumption is not valid unless the wave field is narrow-banded in both frequency

and direction. Thus, for most coastal wave predictions to be accurate, they must solve all wave components

and not just a hypothetical "dominant" component. This presents significant problems for wave models that

solve only one wave component at a time, since wave energy traveling in one direction can be "scattered" into

another direction via diffraction. Hence, diffraction causes wave components in a spectrum to interact and

attempts to solve the CRD equation on a component-by-component basis have difficulty properly accounting

for this effect. STWAVE overcomes this problem by using a piecewise solution method that simulates the

propagation of all wave components simultaneously.

(d) Returning to the second assumption above, field and laboratory data presented in Bouws, Gunther,

and Vincent (1985) and Resio (1988) show that nonconservative effects, rather than conservative propagation

effects, dominate wave transformations in many coastal areas, particularly during storm conditions.

Moreover, the form of many of the source terms affecting shallow-water wave transformations is such that

they depend on energy content within the entire wave spectrum. Methods that solve for each component of

the spectrum independently cannot provide suitable estimates of coupled source terms. STWAVE is

formulated in a manner that permits straightforward solution of these processes.

(2) Examples of STWAVE results. The following comparisons are intended to demonstrate the impor-

tance of various terms in coastal wave transformations and the ability of STWAVE to handle these terms.

(a) Spectral versus monochromatic calculations. Figure II-3-12 compares predicted wave heights behind

a shoal using STWAVE, for a unidirectional, monochromatic wave and for a JONSWAP spectrum with a

spectral peak frequency of 0.1 Hz and a cos4 angular distribution of energy. Monochromatic calculations

from the laboratory study of Vincent and Briggs (1989), while mathematically accurate, do not reasonably

represent propagation effects in a wave spectrum with natural frequency and direction energy spreads.

(b) Effects of coupled source terms. Figure II-3-13 compares spectral transformation over 1:30, 1:100,

and 1:500 slopes for the same JONSWAP spectrum as above with a mean approach angle to the coast of

30 deg, for the case of no source terms and for the case of wave breaking and nonlinear wave-wave

interaction source terms included. This comparison suggests that CRD effects account for only about

5 percent of the total energy variations in coastal waves passing over moderate to shallow slopes. This

finding is consistent with those of Resio (1988) and helps to explain why nearshore wave spectra tend

strongly toward self-similar forms during local storms (Bouws, Gunther, and Vincent 1985; Resio 1987;

Miller and Vincent 1990).

(c) Wind effects. Figure II-3-14 shows the differences in wave transformations with and without a

20-m/sec onshore wind over an offshore profile typical of the U.S. east coast. In this example, waves at the

seaward boundary are set to the same JONSWAP spectrum as Examples 1 and 2. These results show a

marked difference between the two cases. This difference is consistent with theoretically expected wind input

and indicates that, particularly during storm conditions, neglecting wind input can lead to significant

misestimations of wave conditions.

Estimation of Nearshore Waves

II-3-29

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