Because STWAVE is a half-plane model, only winds blowing toward the shore
(+x direction) are included. Wave damping by offshore winds and growth of
offshore-traveling waves are neglected.
Wave-wave interaction and whitecapping. As energy is fed into the waves
from the wind, it is redistributed through nonlinear wave-wave interaction.
Energy is transferred from the peak of the spectrum to lower frequencies
(decreasing the peak frequency or increasing the peak period) and to high
frequencies (where it is dissipated).
In STWAVE, the frequency of the spectral peak is allowed to increase with
fetch (or equivalently propagation time across a fetch). The equation for this rate
of change of fp is given by:
-3 / 7
4/3
9 u*
(f )
= ( f p )i - ς ∆t
7/3
(15)
5 g
p i+1
where the i and i+1 subscripts refer to the grid column indices within STWAVE
and ζ is a dimensionless constant (Resio and Perrie 1989). The energy gained by
the spectrum is distributed within frequencies on the forward face of the
spectrum (frequencies lower than the peak frequency) in a manner that retains the
self-similar shape of the spectrum.
Wave energy is dissipated (most notably in an actively growing wave field)
through energy transferred to high frequencies and dissipated through wave
breaking (whitecapping) and turbulent/viscous effects. There is a dynamic
balance between energy entering the wave field because of wind input and
energy leaving the wave field because of nonlinear fluxes to higher frequencies
(Resio 1987, 1988a). The energy flux to high frequencies is represented in
STWAVE as:
ε g 1 / 2 Et3 t k 9 / 2
o p
ΓE =
(16)
tanh 3 / 4 (k p d )
(Resio 1987), where
ΓE = energy flux
ε = coefficient equal to 30
Etot = total energy in the spectrum divided by (ρw g)
kp = wave number associated with the peak of the spectrum
The energy loss from the spectrum is calculated by multiplying the energy
flux by the equivalent time for the wave to travel across a grid cell (∆t)
(Equation 14) with β equal to 1.0 for the swell portion of the spectrum and
11
Chapter 2 Governing Equations and Numerical Discretization
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