2
Governing Equations and
Numerical Discretization
This chapter gives an overview of the phase-averaged spectral wave model
STWAVE (STeady-state spectral WAVE model) (Resio 1987, 1988a, 1988b;
Davis 1992; Smith, Resio, and Zundel 1999). STWAVE is a steady-state finite-
difference model based on the wave action balance equation. This report
describes STWAVE version 3.0, which includes calculation of radiation stresses
and identification of regions of active wave breaking.
Model Capabilities
The purpose of applying nearshore wave transformation models is to
describe quantitatively the change in wave parameters (wave height, period,
direction, and spectral shape) between the offshore and the nearshore (typically
depths of 40 m or less). In relatively deep water, the wave field is fairly
homogeneous on the scale of kilometers; but in the nearshore, where waves are
strongly influenced by variations in bathymetry, water level, and current, wave
parameters may vary significantly on the scale of tens of meters. Offshore wave
information is typically available from a wave gauge or a global- or regional-
scale wave hindcast or forecast. Nearshore wave information is required for the
design of almost all coastal engineering projects. Waves drive sediment transport
and nearshore currents, induce wave setup and runup, excite harbor oscillations,
or impact coastal structures. The longshore and cross-shore gradients in wave
height and direction can be as important as the magnitude of these parameters for
some coastal design problems.
STWAVE simulates depth-induced wave refraction and shoaling, current-
induced refraction and shoaling, depth- and steepness-induced wave breaking,
diffraction, wind-wave growth, and wave-wave interaction and whitecapping that
redistribute and dissipate energy in a growing wave field.
A wave spectrum is a statistical representation of a wave field.
Conceptually, a spectrum is a linear superposition of monochromatic waves. A
spectrum describes the distribution of wave energy as a function of frequency
(one-dimensional spectrum) or frequency and direction (two-dimensional
spectrum). An example of a one-dimensional wave spectrum is given in
Figure 1. The peak period of the spectrum is the reciprocal of the frequency of
3
Chapter 2 Governing Equations and Numerical Discretization
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