(4) The three models discussed below are all steady-state models. Time-dependent, shallow-water models

are available (Jensen et al. 1987; Demirbilek and Webster 1992a, 1992b). They are not discussed here

because they require extensive sets of meteorological data and cannot be easily applied. The basic

characteristics of the three models discussed are as follows:

(a) (RCPWAVE) RCPWAVE is a steady-state, linear-wave model based on the mild-slope equation and

includes wave breaking. It is applicable for open coast areas without structures. It is basically a

monochromatic-wave approach.

(b) (REFDIF1) REFDIF is a steady-state model based on the parabolic approximation solution to the

mild-slope equation. The model includes wave breaking, wave damping, and some nonlinear effects.

Although primarily used as a monochromatic wave model, a spectral version is available. The model can

simulate aspects of propagation associated with simple currents and can include structures.

(c) (STWAVE) STWAVE is a steady-state, linear wave model that computes the evolution of the

directional spectrum over space (Equation II-3-1). The model includes breaking, bottom friction, percolation,

and wind input and solves for the nonlinear transfers of energy within the wave spectrum. It has two modes

for handling diffraction of wave energy and the computational domain may include simple structures. The

models can handle aspects of propagation associated with simple currents.

(5) The three models are theoretically complicated and computationally demanding. All can be

effectively used on a powerful PC-type computer or work station. Each model has considerable strengths and

each can be an appropriate choice for wave transformation. However, none can be considered universally

applicable and the results from all can be inaccurate if the assumptions made in model development are

significantly violated. Users of any of the models must become thoroughly familiar with the model, its

assumptions, and limitations.

(1) Introduction.

(a) The RCPWAVE model (Ebersole 1985; Ebersole, Cialone, and Prater 1986) was developed in the

early 1980's as an engineering tool for calculating the properties of waves as they propagate into shallow

water and eventually break. The theoretical basis for the model (linear-wave theory) and the types of

information generated by the model (wave height, period, and direction as a function of location) are

consistent with current theories and equations used by the engineering community to calculate potential

longshore sand-transport rates and shoreline and beach change. The model was designed to operate

efficiently for coastal regions that may be tens of kilometers in length, and to overcome deficiencies of

previously developed refraction models that could be applied on a regional scale. The wave ray refraction

models of Harrison and Wilson (1964), Dobson (1967), Noda et al. (1974), and others "failed" in regions of

strong wave convergence and divergence (i.e., highly irregular bathymetry), leaving users with no wave

solutions and little guidance for interpreting results in these regions. Berkhoff (1972, 1976) derived an

elliptic equation that approximately represented the complete transformation process for linear waves over

arbitrary bathymetry, where the bathymetry was only constrained to have mild slopes. Numerical solution

of this equation requires discretization of the spatial domain and subsequent computations with grid

resolutions that are a fraction of the wave lengths being considered (typically one tenth or smaller). This

requirement limits the utility of the approach for large regions of coastline.

(b) RCPWAVE is based on the mild-slope equation. An assumed form for the velocity potential

associated with only the forward scattered wave field is used with the mild slope equation to develop two

equations, one describing the conservation of wave energy (assuming a constant wave frequency) and the

II-3-20

Estimation of Nearshore Waves

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