0.9 for the sea portion of the spectrum. This dissipation is only applied in the
model if wind input is included.
Radiation stress gradients
Gradients in radiation stress are calculated in STWAVE to provide wave
forcing to external circulation models to drive nearshore currents and water level
changes (i.e., wave setup and setdown). Wave-driven currents are generally the
dominant forcing for sediment transport in the surf zone. Radiation stress tensors
are calculated based on linear wave theory:
(
)
2kd
∫∫
S xx = ρ w g
E ( f ,α )0.5 1 +
cos α + 1 - 0.5 dfdα
2
(17)
sinh2kd
E ( f ,α )
2kd
∫∫
sin 2α dfdα
0.5 1 +
S xy = ρ w g
(18)
sinh 2kd
2
(
)
2kd
∫∫
sin 2α + 1 - 0.5 dfdα
E ( f ,α) 0.5 1 +
S yy = ρ w g
(19)
sinh 2kd
The gradients in radiation stress are calculated as:
∂S xx ∂S xy
τx = -
-
(20)
∂x
∂y
∂S xy
∂S yy
τy =-
-
(21)
∂x
∂y
Values of τx /ρw and τy/ρw are output from STWAVE for use in circulation
modeling.
Numerical Discretization
STWAVE is a finite-difference numerical model, formulated on a Cartesian
grid. Grid cells are square (∆x = ∆y). Variable grid resolution can be obtained
by nesting model runs. This is accomplished by running the model at a coarse
resolution and saving a spectrum at a nearshore point. This nearshore spectrum
can then be used as a boundary condition for another grid of finer resolution. A
schematic of a grid is shown in Figure 3. STWAVE operates in a local
coordinate system, with the x-axis oriented in the cross-shore direction (origin
offshore) and the y-axis oriented alongshore, forming a right-handed coordinate
system. The orientation of the x-axis (87.5 deg) defines the half plane that is
12
Chapter 2 Governing Equations and Numerical Discretization
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